Enabled reconstruction of the total flux for rotated HDG.

Minor formatting.
Fixed assembly of LDG faces.
2025-08-18 17:56:10 -07:00 · 2025-08-16 09:48:03 -07:00 · 2025-08-13 23:03:17 -07:00 · 2025-08-13 17:11:22 -07:00 · 2025-08-13 15:31:38 -07:00 · 2025-08-13 15:29:56 -07:00
625 changed files with 58739 additions and 40126 deletions
@@ -1,154 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: Sanitizer Config
-description: Sets up environment variables for MFEM sanitizer workflow
-
-inputs:
-  DEBUG:
-    description: If true, use intermediate caches to speed up the workflow
-                 by reusing previous builds.
-    default: false
-
-  REPOSITORY:
-    description: Repository to checkout
-    default: mfem/mfem
-
-  BRANCH:
-    description: Branch to checkout
-    default: ubsan
-
-  CLANG_VER:
-    description: CLANG version to use
-    default: 18
-
-  # https://github.com/llvm/llvm-project/releases
-  LLVM_VER:
-    description: LLVM version to use
-    default: 19.1.7
-
-  # https://github.com/hypre-space/hypre/releases
-  HYPRE_VER:
-    description: HYPRE version to use
-    default: 2.19.0
-
-  METIS_VER:
-    description: METIS version to use
-    default: 4.0.3
-
-  CTEST:
-    description: CTest command to use
-    default: ctest -j --test-load $(nproc)
-                      --schedule-random
-                      --stop-on-failure --output-on-failure
-                      --test-dir
-
-  # https://clang.llvm.org/docs/AddressSanitizer.html
-  ASAN_OPTIONS:
-    default: detect_leaks=1,
-             strict_init_order=1,
-             strict_string_checks=1,
-             check_initialization_order=1,
-             detect_stack_use_after_return=1
-  ASAN_CXXFLAGS:
-    default: -fsanitize=address
-             -fsanitize-address-use-after-scope
-  ASAN_LDFLAGS:
-    default: -fsanitize=address
-
-  # https://clang.llvm.org/docs/UndefinedBehaviorSanitizer.html
-  UBSAN_OPTIONS:
-    default: halt_on_error=1, print_stacktrace=1
-  UBSAN_CXXFLAGS:
-    default: -fsanitize=undefined
-  UBSAN_LDFLAGS:
-    default: -fsanitize=undefined
-
-  # https://clang.llvm.org/docs/MemorySanitizer.html
-  MSAN_OPTIONS:
-    default: "poison_in_dtor=1"
-  MSAN_CXXFLAGS:
-    default: -fsanitize=memory
-             -fsanitize-memory-track-origins
-             -fsanitize-memory-use-after-dtor
-  MSAN_LDFLAGS:
-    default: -fsanitize=memory
-
-  LSAN_DIR:
-    description: LSAN suppression directory
-    default: lsan
-
-  LSAN_FILE:
-    description: LSAN suppression file
-    default: lsan.supp
-
-  NO_FLAGS:
-    description: If true, do not set any CXXFLAGS or LDFLAGS.
-    default: false
-
-runs:
-  using: 'composite'
-  steps:
-    - name: Env (Inputs)
-      run: |
-        echo DEBUG=${{inputs.DEBUG}} >> $GITHUB_ENV
-        echo REPOSITORY=${{inputs.REPOSITORY}} >> $GITHUB_ENV
-        echo BRANCH=${{inputs.BRANCH}} >> $GITHUB_ENV
-        echo CLANG_VER=${{inputs.CLANG_VER}} >> $GITHUB_ENV
-        echo LLVM_VER=${{inputs.LLVM_VER}} >> $GITHUB_ENV
-        echo HYPRE_VER=${{inputs.HYPRE_VER}} >> $GITHUB_ENV
-        echo METIS_VER=${{inputs.METIS_VER}} >> $GITHUB_ENV
-        echo CTEST=${{inputs.CTEST}} >> $GITHUB_ENV
-        echo ASAN_OPTIONS=${{inputs.ASAN_OPTIONS}} >> $GITHUB_ENV
-        echo UBSAN_OPTIONS=${{inputs.UBSAN_OPTIONS}} >> $GITHUB_ENV
-        echo MSAN_OPTIONS=${{inputs.MSAN_OPTIONS}} >> $GITHUB_ENV
-        echo LSAN_DIR=${{inputs.LSAN_DIR}} >> $GITHUB_ENV
-        echo LSAN_FILE=${{inputs.LSAN_FILE}} >> $GITHUB_ENV
-        echo ASAN_CXXFLAGS=${{inputs.ASAN_CXXFLAGS}} >> $GITHUB_ENV
-        echo ASAN_LDFLAGS=${{inputs.ASAN_LDFLAGS}} >> $GITHUB_ENV
-        echo UBSAN_CXXFLAGS=${{inputs.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
-        echo UBSAN_LDFLAGS=${{inputs.UBSAN_LDFLAGS}} >> $GITHUB_ENV
-        echo MSAN_CXXFLAGS=${{inputs.MSAN_CXXFLAGS}} >> $GITHUB_ENV
-        echo MSAN_LDFLAGS=${{inputs.MSAN_LDFLAGS}} >> $GITHUB_ENV
-      shell: bash
-
-    - name: Env (dir)
-      run: |
-        echo LLVM_DIR=${{github.workspace}}/llvm >> $GITHUB_ENV
-        echo HYPRE_DIR=hypre-${{inputs.HYPRE_VER}} >> $GITHUB_ENV
-        echo METIS_DIR=metis-${{inputs.METIS_VER}} >> $GITHUB_ENV
-      shell: bash
-
-    - name: Env (bis)
-      run: |
-        echo CC=clang-${{inputs.CLANG_VER}} >> $GITHUB_ENV
-        echo CXX=clang++-${{inputs.CLANG_VER}} >> $GITHUB_ENV
-        echo LLVM_INC=${{env.LLVM_DIR}}/include/c++/v1 >> $GITHUB_ENV
-        echo LLVM_LIB=${{env.LLVM_DIR}}/lib >> $GITHUB_ENV
-        echo HYPRE_TGZ=v${{inputs.HYPRE_VER}}.tar.gz >> $GITHUB_ENV
-        echo METIS_TGZ=metis-${{inputs.METIS_VER}}.tar.gz >> $GITHUB_ENV
-        LSAN_SUPPRESSIONS="${{github.workspace}}/${{inputs.LSAN_DIR}}/${{inputs.LSAN_FILE}}"
-        echo "LSAN_OPTIONS=suppressions=$LSAN_SUPPRESSIONS" >> $GITHUB_ENV
-      shell: bash
-
-    - name: Env (ter)
-      if: ${{ inputs.NO_FLAGS != 'true' }}
-      run: |
-        echo LLVM_CXXFLAGS=-stdlib=libc++ -I${{env.LLVM_INC}} -Isystem${{env.LLVM_INC}} >> $GITHUB_ENV
-        echo LLVM_LDFLAGS=-L${{env.LLVM_LIB}} -lc++abi -Wl,-rpath,${{env.LLVM_LIB}} >> $GITHUB_ENV
-      shell: bash
-
-    - name: Env (quater)
-      if: ${{ inputs.NO_FLAGS != 'true' }}
-      run: |
-        echo CXXFLAGS=${{env.LLVM_CXXFLAGS}} >> $GITHUB_ENV
-        echo LDFLAGS=${{env.LLVM_LDFLAGS}} >> $GITHUB_ENV
-      shell: bash
@@ -1,91 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: 'MFEM Compilation'
-description: 'MFEM Compilation'
-
-inputs:
-  par:
-    description: 'Whether to build for parallel (true/false)'
-    default: false
-  sanitizer:
-    description: 'Sanitizer to use (asan, msan, ubsan)'
-    default: asan
-
-runs:
-  using: 'composite'
-  steps:
-    - uses: ./.github/actions/sanitize/config
-
-    - uses: actions/cache@v4
-      if: ${{env.DEBUG == 'true'}}
-      id: debug
-      with:
-        path: mfem/build
-        key: build-${{inputs.par}}-${{inputs.sanitizer}}
-
-    - uses: ./.github/actions/sanitize/setup
-      if: ${{steps.debug.outputs.cache-hit != 'true'}}
-      with:
-        par: ${{inputs.par}}
-        sanitizer: ${{inputs.sanitizer}}
-
-    - name: Build with ASAN
-      if: inputs.sanitizer == 'asan'
-      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.ASAN_CXXFLAGS}} >> $GITHUB_ENV
-      shell: bash
-
-    - name: Build with MSAN
-      if: inputs.sanitizer == 'msan'
-      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.MSAN_CXXFLAGS}} >> $GITHUB_ENV
-      shell: bash
-
-    - name: Build with UBSAN
-      if: inputs.sanitizer == 'ubsan'
-      run: echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.UBSAN_CXXFLAGS}} >> $GITHUB_ENV
-      shell: bash
-
-    - uses: mfem/github-actions/build-mfem@v2.5
-      if: ${{steps.debug.outputs.cache-hit != 'true'}}
-      env:
-        CXXFLAGS: ${{env.CXXFLAGS}}
-        LDFLAGS: ${{env.LDFLAGS}}
-      with:
-        mpi: ${{inputs.par == 'false' && 'seq' || 'par'}}
-        mfem-dir: mfem
-        os: ${{runner.os}}
-        library-only: true
-        build-system: cmake
-        hypre-dir: ${{env.HYPRE_DIR}}
-        metis-dir: ${{env.METIS_DIR}}
-        config-options: >-
-          -GNinja
-          -DMPICXX=${{env.CXX}}
-          -DCMAKE_CXX_STANDARD=17
-          -DMFEM_USE_MEMALLOC=OFF
-          -DCMAKE_BUILD_TYPE=Release
-          -DCMAKE_VERBOSE_MAKEFILE=ON
-          -DCMAKE_CXX_COMPILER=${{env.CXX}}
-          -DCMAKE_CXX_FLAGS_RELEASE='-g -O1 -fno-omit-frame-pointer'
-
-    - name: Delete object files
-      if: ${{steps.debug.outputs.cache-hit != 'true'}}
-      working-directory: mfem/build
-      run: find . -type f -name '*.o' -delete
-      shell: bash
-
-    - uses: actions/upload-artifact@v4
-      with:
-        name: build-${{inputs.par}}-${{inputs.sanitizer}}
-        path: mfem/build
-        if-no-files-found: error
-        retention-days: 1
-        overwrite: false
@@ -1,33 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: 'Install MPI'
-description: 'Installs MPI and set up its environment variables'
-
-runs:
-  using: 'composite'
-  steps:
-    - name: Install
-      run: sudo apt-get install openmpi-bin libopenmpi-dev
-      shell: bash
-
-    - name: Env
-      run: |
-        echo PRTE_MCA_rmaps_default_mapping_policy=:oversubscribe >> $GITHUB_ENV
-        echo MPI_INC=$(mpicxx --showme:compile) >> $GITHUB_ENV
-        echo MPI_LIB=$(mpicxx --showme:link) >> $GITHUB_ENV
-      shell: bash
-
-    - name: Env (bis)
-      run: |
-        echo CXXFLAGS=${{env.CXXFLAGS}} ${{env.MPI_INC}} >> $GITHUB_ENV
-        echo LDFLAGS=${{env.LDFLAGS}} ${{env.MPI_LIB}} >> $GITHUB_ENV
-      shell: bash
@@ -1,71 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: 'Restore state'
-description: 'Restore state to be able to run checks, tests'
-
-inputs:
-  par:
-    description: 'Whether to build for parallel (true/false)'
-    default: false
-  sanitizer:
-    description: 'Sanitizer to use (asan, msan, ubsan)'
-    default: asan
-  cache-path:
-    description: 'path to what needs to be restored'
-    default: none
-  cache-skip:
-    description: 'Skip cache restoration'
-    default: false
-
-outputs:
-  cache-hit:
-    description: 'Output from a specific step'
-    value: ${{steps.debug.outputs.cache-hit}}
-
-runs:
-  using: 'composite'
-  steps:
-    - uses: ./.github/actions/sanitize/config
-
-    - uses: actions/cache@v4
-      if: ${{env.DEBUG == 'true' && inputs.cache-skip != 'true'}}
-      id: debug
-      with:
-        path: ${{inputs.cache-path}}
-        key: ${{github.job}}-${{inputs.par}}-${{inputs.sanitizer}}
-
-    - uses: ./.github/actions/sanitize/setup
-      if: ${{steps.debug.outputs.cache-hit != 'true'}}
-      with:
-        par: ${{inputs.par}}
-        sanitizer: ${{inputs.sanitizer}}
-
-    - uses: actions/download-artifact@v4
-      with:
-        name: build-${{inputs.par}}-${{inputs.sanitizer}}
-        path: mfem/build
-
-    - name: Ninja Patch
-      working-directory: mfem/build
-      run: |
-        sed -i -e 's/CXX_STATIC_LIBRARY_LINKER__mfem_Release.*/CUSTOM_COMMAND/' build.ninja
-        sed -i -e '/build tests\/unit\/all:/ s/tests\/unit\/[^ ]*unit_tests[^ ]*//g' build.ninja
-        sed -i -e '/^add_test(\[=\[\(unit_tests\|punit_tests\)\]=\]/ s/)/ "--input-file .\/list-test-names-${{matrix.tag}}" "--min-duration 1")/' tests/unit/CTestTestfile.cmake
-      shell: bash
-
-    - name: Copy Data
-      if: ${{steps.debug.outputs.cache-hit != 'true'}}
-      working-directory: mfem/build
-      run: |
-        ninja cmake_object_order_depends_target_unit_tests
-        cp -pR ../tests/unit/data tests/unit
-      shell: bash
@@ -1,64 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: 'Setup state'
-description: 'Sets up the state to be able to run build & run'
-
-inputs:
-  par:
-    description: 'Whether to build for parallel (true/false)'
-    default: false
-  sanitizer:
-    description: 'Sanitizer to use (asan, msan, ubsan)'
-    default: asan
-
-runs:
-  using: 'composite'
-  steps:
-    - uses: actions/cache/restore@v4  # Cache for LLVM libcxx
-      with:
-        path: ${{env.LLVM_DIR}}
-        fail-on-cache-miss: true
-        key: build-libcxx-${{env.LLVM_VER}}-${{inputs.sanitizer}}
-
-    - uses: ./.github/actions/sanitize/mpi
-      if: ${{inputs.par == 'true'}}
-
-    - uses: actions/cache/restore@v4  # Cache for Hypre
-      if: ${{inputs.par == 'true'}}
-      with:
-        path: ${{env.HYPRE_DIR}}
-        fail-on-cache-miss: true
-        key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
-
-    - uses: actions/cache/restore@v4  # Cache for Metis
-      if: ${{inputs.par == 'true'}}
-      with:
-        path: ${{env.METIS_DIR}}
-        fail-on-cache-miss: true
-        key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
-
-    - name: Hypre/Metis links
-      if: ${{inputs.par == 'true'}}
-      run: ln -s -f ${{env.HYPRE_DIR}} hypre && ln -s -f ${{env.METIS_DIR}} metis-4.0
-      shell: bash
-
-    - uses: actions/cache/restore@v4  # Cache for LSAN suppression file
-      with:
-        path: ${{env.LSAN_DIR}}
-        fail-on-cache-miss: true
-        key: build-lsan-suppression-file
-
-    - uses: actions/checkout@v4  # Checkout the repository
-      with:
-        path: mfem
-        # ref: ${{env.BRANCH}}
-        # repository: ${{env.REPOSITORY}}
@@ -7,17 +7,18 @@

                               https://mfem.org

+
 This directory contains the GitHub CI scripts for MFEM.

 Note that some of these scripts use the shared MFEM GitHub Actions from the external mfem/github-actions repository:

-  <https://github.com/mfem/github-actions>
+  https://github.com/mfem/github-actions

-For a particular action, e.g. `mfem/github-actions/build-mfem@v2.5`, the `v2.5` suffix denotes the branch in the above from which the action is taken.
+For a particular action, e.g. `mfem/github-actions/build-mfem@v2.1`, the `v2.1` suffix denotes the branch in the above from which the action is taken.

 The current CI workflows are:

-## `repo-check.yml`
+### `repo-check.yml`

 Runs a number of static repository-level sanity checks.

@@ -29,39 +30,19 @@ Runs a number of static repository-level sanity checks.

 - `branch-history` guards against accidental commits of large files using the `--history` option of the `config/githooks/pre-push` script.

-## `mfem-analysis.yml` (`build-analysis`)
+### `mfem-analysis.yml` (`build-analysis`)

 Checks if the code builds and satisfies minimal requirements.

 - `gitignore` builds hypre, METIS, and MFEM using `mfem/github-actions/build-hypre`, `mfem/github-actions/build-metis`, and `mfem/github-actions/build-mfem` and checks for correct `.gitignore` settings by running the `tests/scripts/gitignore` script.

-## `builds-and-tests.yml`
+### `builds-and-tests.yml`

 Runs a matrix of builds and tests runs with different compilers, OS, mfem/hypre settings, etc. Also processes and upload Codecov reports.

-Uses the following GitHub Actions from <https://github.com/mfem/github-actions>:
+Uses the following GitHub Actions from https://github.com/mfem/github-actions:

 - `mfem/github-actions/build-hypre`
 - `mfem/github-actions/build-metis`
 - `mfem/github-actions/build-mfem`
 - `mfem/github-actions/upload-coverage`
-
-## Sanitizer Workflow for MFEM Verification
-
-This workflow validates MFEM unit tests, examples, and miniapps using sanitizer tools.
-
- `sanitizers.yml` orchestrates:
-  - Building and caching dependencies: HYPRE, METIS, LSAN suppression file, and LLVM libcxx.
-  - Launching fine-grained jobs for serial (ASAN, MSAN, UBSAN) and parallel (ASAN, UBSAN) sanitizers.
- `sanitize-tests.yml` is a reusable workflow accepting `par` mode (`true` for parallel) and `sanitizer` (ASAN, MSAN, or UBSAN) as inputs. It executes the following jobs:
-  - **Build**: Compiles the MFEM library with specified parallel and sanitizer settings.
-  - **Check**: Runs verification checks.
-  - Parallel jobs to test the following: **Examples**, **Miniapps** and **Unit tests**
-
-The workflow leverages composite actions in `.github/actions/sanitize/`:
-
- `config`: Centralizes settings for the sanitizer workflow.
- `mfem`: Manages the MFEM library build process.
- `mpi`: Installs MPI and applies additional compilation flags.
- `restore`: Restores the testing environment state.
- `setup`: Builds or restores cached dependencies.
@@ -58,7 +58,6 @@ jobs:
        build-system: [make, cmake]
        hypre-target: [int32]
        precision: [fp64]
-        enzyme: [false]
        exclude:
          - os: ubuntu-latest
            build-system: cmake
@@ -81,17 +80,15 @@ jobs:
            codecov: YES
          - os: ubuntu-latest
            target: dbg
-            config-opts: "CPPFLAGS+=-Og"
+            config-opts: 'CPPFLAGS+=-Og'
          - os: macos-latest
            codecov: NO
          - os: windows-latest
            codecov: NO
-            # config-opts: '-G "Ninja Multi-Config"'
          - os: windows-latest
            target: opt
            mpi: par
-            config-opts: "-DBUILD_SHARED_LIBS=ON"
-            # config-opts: '-DBUILD_SHARED_LIBS=ON -G "Ninja Multi-Config"'
+            config-opts: '-DBUILD_SHARED_LIBS=ON'
          - os: ubuntu-latest
            target: opt
            codecov: NO
@@ -99,7 +96,7 @@ jobs:
            build-system: cmake
            hypre-target: int32
            precision: fp64
-            config-opts: "-DCMAKE_INSTALL_PREFIX=../cmake-install"
+            config-opts: '-DCMAKE_INSTALL_PREFIX=../cmake-install'
            # This option can be set to pass additional configuration options to
            # the MFEM configuration command.
            # config-opts: '-DCMAKE_VERBOSE_MAKEFILE=ON'
@@ -124,30 +121,18 @@ jobs:
            build-system: make
            hypre-target: int32
            precision: fp32
-          - os: macos-latest
-            target: opt
-            codecov: NO
-            mpi: par
-            build-system: make
-            hypre-target: int32
-            precision: fp64
-            enzyme: true
-            config-opts: MFEM_USE_ENZYME=YES ENZYME_DIR=$(brew --prefix enzyme) LDFLAGS=-L$LLVM_PREFIX/lib/c++
-
-    name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}${{ matrix.enzyme && '-enzyme' || '' }}
+    name: ${{ matrix.os }}-${{ matrix.build-system }}-${{ matrix.target }}-${{ matrix.mpi }}-${{ matrix.hypre-target }}-${{ matrix.precision }}

    runs-on: ${{ matrix.os }}

-    continue-on-error: ${{ matrix.enzyme && true || false }}
-
    steps:
      # Fix 'No space left on device' errors for Ubuntu builds.
      - name: Run Actions Cleaner
        if: matrix.os == 'ubuntu-latest'
        uses: easimon/maximize-build-space@v8
        with:
-          overprovision-lvm: "true"
-          remove-android: "true"
+          overprovision-lvm: 'true'
+          remove-android: 'true'

      # Checkout MFEM in "mfem" subdirectory. Final path:
      # /home/runner/work/mfem/mfem/mfem
@@ -159,24 +144,10 @@ jobs:
          # Fetch the complete history for codecov to access commits ID
          fetch-depth: 0

-      - name: Windows environment - PowerShell [debug]
-        if: matrix.os == 'windows-latest'
-        run: |
-          ls env: | fl
-
-      - name: Windows environment - Bash [debug]
-        if: matrix.os == 'windows-latest'
-        run: |
-          env
-        shell: bash
-
-      # For info on Xcode see:
-      #  - https://github.com/actions/runner-images/issues/12541
-      #  - https://github.com/actions/runner-images/blob/releases/macos-15-arm64/20250811/images/macos/macos-15-arm64-Readme.md#xcode
      - name: Xcode version setup (MacOS)
        if: matrix.os == 'macos-latest'
        run: |
-          XCODE_PATH="/Applications/Xcode_16.4.app"
+          XCODE_PATH="/Applications/Xcode_15.3.app"
          echo "> sudo xcode-select -s ${XCODE_PATH}"
          sudo xcode-select -s ${XCODE_PATH}
          echo "> g++ -v"
@@ -287,20 +258,6 @@ jobs:
        run: |
          vcpkg install metis-mfem --triplet=x64-windows-static --overlay-ports=${{ env.MFEM_TOP_DIR }}/config/vcpkg/ports

-      # It's usually fine to build the above TPLs with a different compiler.
-      #
-      - name: install Enzyme (macOS w/ Enzyme)
-        if: matrix.enzyme && matrix.os == 'macos-latest'
-        run: |
-          export HOMEBREW_NO_INSTALL_CLEANUP=1
-          brew update
-          brew install enzyme
-          ENZYME_LLVM=$(brew info enzyme | sed -n 's/^Required:.*\(llvm[^ ]*\).*/\1/p')
-          LLVM_PREFIX=$(brew --prefix $ENZYME_LLVM)
-          echo "LLVM_PREFIX=$LLVM_PREFIX" >> $GITHUB_ENV
-          echo "OMPI_CC=$LLVM_PREFIX/bin/clang" >> $GITHUB_ENV
-          echo "OMPI_CXX=$LLVM_PREFIX/bin/clang++" >> $GITHUB_ENV
-
      # MFEM build and test
      - name: build
        uses: mfem/github-actions/build-mfem@v2.5
@@ -45,15 +45,14 @@ jobs:

      - name: Get MPI (Linux)
        run: |
-          sudo apt-get install openmpi-bin libopenmpi-dev
-          export OMPI_MCA_rmaps_base_oversubscribe=1
+          sudo apt-get install mpich libmpich-dev

      - name: Cache Hypre Install
        id: hypre-cache
        uses: actions/cache@v4
        with:
          path: ${{ env.HYPRE_TOP_DIR }}
-          key: ${{ runner.os }}-ompi-build-${{ env.HYPRE_TOP_DIR }}-v2.5
+          key: ${{ runner.os }}-build-${{ env.HYPRE_TOP_DIR }}-v2.5

      - name: Get Hypre
        if: steps.hypre-cache.outputs.cache-hit != 'true'
@@ -0,0 +1,69 @@
+# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+name: "Sanitizer"
+
+permissions:
+  actions: write
+
+on:
+  push:
+    branches:
+      - master
+      - next
+  pull_request:
+  workflow_dispatch:
+
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
+jobs:
+  Serial:
+    runs-on: ubuntu-24.04
+
+    steps:
+      - name: MFEM Checkout
+        uses: actions/checkout@v4
+        with:
+          path: mfem
+
+      - name: MFEM Build
+        uses: mfem/github-actions/build-mfem@v2.5
+        with:
+          os: ${{ runner.os }}
+          target: opt
+          mpi: seq
+          hypre-dir: unused-hypre-dir
+          metis-dir: unused-metis-dir
+          mfem-dir: mfem
+          build-system: make
+          library-only: false
+          config-options:
+            CXX="clang++-18"
+            CXXFLAGS="-g -O1 -std=c++11
+                      -fsanitize=address
+                      -fno-omit-frame-pointer
+                      -fsanitize-address-use-after-scope"
+
+      - name: MFEM Info
+        working-directory: mfem
+        run: make info
+
+      - name: MFEM Sanitize
+        working-directory: mfem
+        run:
+          ASAN_OPTIONS="detect_leaks=1,
+                        strict_init_order=1,
+                        strict_string_checks=1,
+                        check_initialization_order=1,
+                        detect_stack_use_after_return=1"
+          make test
@@ -1,39 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: build-hypre
-on:
-  workflow_call:
-jobs:
-  build-hypre:
-    runs-on: ubuntu-latest
-    name: 2.19.0
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/config
-      - name: Cache
-        id: cache
-        uses: actions/cache@v4
-        with:
-          path: ${{env.HYPRE_DIR}}
-          key: ${{runner.os}}-ompi-build-${{env.HYPRE_DIR}}-int32-fp64-v2.5
-      - name: Setup
-        if: steps.cache.outputs.cache-hit != 'true'
-        uses: ./.github/actions/sanitize/mpi
-      - name: Build
-        if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-hypre@v2.5
-        with:
-          archive: ${{env.HYPRE_TGZ}}
-          dir: ${{env.HYPRE_DIR}}
-          target: int32
-          precision: fp64
-          build-system: make
@@ -1,76 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: build-libcxx
-on:
-  workflow_call:
-jobs:
-  build-llvm-libcxx:
-    runs-on: ubuntu-latest
-    strategy:
-      matrix:
-        sanitizer: [asan, msan, ubsan]
-        include:
-          - sanitizer: asan
-            llvm_use_sanitizer: "Address"
-          - sanitizer: msan
-            llvm_use_sanitizer: "MemoryWithOrigins"
-          - sanitizer: ubsan
-            llvm_use_sanitizer: "Undefined"
-    name: ${{matrix.sanitizer}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/config
-        with:
-          NO_FLAGS: true
-      - name: Cache
-        id: cache
-        uses: actions/cache@v4
-        with:
-          path: ${{env.LLVM_DIR}}
-          key: build-libcxx-${{env.LLVM_VER}}-${{matrix.sanitizer}}
-      - name: Clone
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        run: >
-          git clone --filter=blob:none --depth=1
-          --branch llvmorg-${{env.LLVM_VER}}
-          --no-checkout https://github.com/llvm/llvm-project.git llvm-project
-      - name: Checkout
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        working-directory: llvm-project
-        run: |
-          git sparse-checkout set --cone
-          git checkout llvmorg-${{env.LLVM_VER}}
-          git sparse-checkout set cmake llvm/cmake runtimes libcxx libcxxabi
-      - name: Mkdir
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        run: mkdir ${{env.LLVM_DIR}}
-      - name: CMake
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        working-directory: ${{env.LLVM_DIR}}
-        run: >
-          VERBOSE=1
-          cmake -GNinja ../llvm-project/runtimes/
-          -DCMAKE_C_COMPILER=${{env.CC}}
-          -DCMAKE_CXX_COMPILER=${{env.CXX}}
-          -DCMAKE_BUILD_TYPE=RelWithDebInfo
-          -DCMAKE_INSTALL_PREFIX=/usr
-          -DLLVM_USE_SANITIZER=${{matrix.llvm_use_sanitizer}}
-          -DLLVM_BUILD_32_BITS=OFF
-          -DLIBCXXABI_USE_LLVM_UNWINDER=OFF
-          -DLLVM_INCLUDE_TESTS=OFF
-          -DLIBCXX_INCLUDE_TESTS=OFF
-          -DLIBCXX_INCLUDE_BENCHMARKS=OFF
-          -DLLVM_ENABLE_RUNTIMES='libcxx;libcxxabi'
-      - name: Build
-        if: ${{ steps.cache.outputs.cache-hit != 'true' }}
-        working-directory: ${{env.LLVM_DIR}}
-        run: cmake --build . -- cxx cxxabi
@@ -1,38 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: build-file-lsan
-on:
-  workflow_call:
-jobs:
-  build-file-lsan:
-    runs-on: ubuntu-latest
-    name: lsan.supp
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/config
-      - name: Cache
-        id: cache
-        uses: actions/cache@v4
-        with:
-          path: ${{env.LSAN_DIR}}
-          key: build-lsan-suppression-file
-      - name: Setup
-        if: steps.cache.outputs.cache-hit != 'true'
-        run: |
-          mkdir -p ${{env.LSAN_DIR}}
-          cat << EOF > ${{env.LSAN_DIR}}/${{env.LSAN_FILE}}
-          leak:libevent_core-2.1.so
-          leak:ompi_mpi_finalize
-          leak:ompi_mpi_init
-          leak:PMPI_Init
-          leak:strdup
-          EOF
@@ -1,36 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: build-metis
-on:
-  workflow_call:
-jobs:
-  build-metis:
-    runs-on: ubuntu-latest
-    name: 4.0.3
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/config
-      - name: Cache
-        id: cache
-        uses: actions/cache@v4
-        with:
-          path: ${{env.METIS_DIR}}
-          key: ${{runner.os}}-build-${{env.METIS_DIR}}-v2.5
-      - name: Setup
-        if: steps.cache.outputs.cache-hit != 'true'
-        uses: ./.github/actions/sanitize/mpi
-      - name: Build
-        if: steps.cache.outputs.cache-hit != 'true'
-        uses: mfem/github-actions/build-metis@v2.5
-        with:
-          archive: ${{env.METIS_TGZ}}
-          dir: ${{env.METIS_DIR}}
@@ -1,197 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: Sanitize
-on:
-  workflow_call:
-    inputs:
-      par:
-        description: 'Whether to build for parallel (true/false)'
-        required: false
-        default: false
-        type: boolean
-      sanitizer:
-        description: 'Sanitizer to use (asan, msan, ubsan)'
-        required: true
-        default: asan
-        type: string
-
-jobs:
-  build:
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/mfem
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-
-  check:
-    needs: [build]
-    runs-on: ubuntu-latest
-    env:
-      ex: ${{inputs.par && 'ex1p' || 'ex1'}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/examples/${{env.ex}}
-      - name: MFEM Check
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: ninja -v check
-
-  examples:
-    needs: [check]
-    runs-on: ubuntu-latest
-    env:
-      exclude: ${{inputs.par && '-E "_ser"' || ''}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/examples/ex1
-      - name: Build Examples
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: ninja -v examples
-      - name: Test Examples
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: |
-          ${{env.CTEST}} examples ${{env.exclude}} --show-only
-          ${{env.CTEST}} examples ${{env.exclude}}
-
-  miniapps:
-    needs: [check]
-    runs-on: ubuntu-latest
-    env:
-      exclude: ${{inputs.par && '-E "_ser"' || ''}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/miniapps/meshing/minimal-surface
-      - name: Build Miniapps
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: ninja -v miniapps
-      - name: Test Miniapps
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: |
-          ${{env.CTEST}} miniapps ${{env.exclude}} --show-only
-          ${{env.CTEST}} miniapps ${{env.exclude}}
-
-  tests-miniapps:
-    needs: [check]
-    runs-on: ubuntu-latest
-    env:
-      run: ${{inputs.par && '-R "_cpu_np"' || ''}}
-      exclude: ${{inputs.par && '"unit_tests|debug"' || '"^unit_tests$|debug"'}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/tests/unit/sedov_tests_cpu
-      - name: Build Tests Unit Miniapps
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: ninja -v tests/unit/all
-      - name: Run Tests Unit Miniapps
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: |
-          ${{env.CTEST}} tests/unit -E ${{env.exclude}} ${{env.run}} --show-only
-          ${{env.CTEST}} tests/unit -E ${{env.exclude}} ${{env.run}}
-
-  tests-unit-build:
-    needs: [check]
-    runs-on: ubuntu-latest
-    env:
-      unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/tests/unit/${{env.unit_tests}}
-      - name: Build Unit Tests
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: ninja -v ${{env.unit_tests}}
-      - name: Delete object files
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build/tests/unit
-        run: find . -type f -name '*.o' -delete
-      - uses: actions/upload-artifact@v4
-        with:
-          name: tests-${{inputs.par}}-${{inputs.sanitizer}}
-          path: mfem/build/tests/unit/${{env.unit_tests}}
-          if-no-files-found: error
-          retention-days: 1
-          overwrite: false
-
-  tests-unit-run:
-    needs: [tests-unit-build]
-    runs-on: ubuntu-latest
-    strategy:
-      matrix:
-        tag: [0, 1, 2, 3]
-    name: tests-unit-run-${{matrix.tag}}
-    env:
-      unit_tests: ${{inputs.par && 'punit_tests' || 'unit_tests'}}
-      np: ${{inputs.par && '_np=2' || ''}}
-    steps:
-      - uses: actions/checkout@v4
-      - uses: ./.github/actions/sanitize/restore
-        id: restore
-        with:
-          par: ${{inputs.par}}
-          sanitizer: ${{inputs.sanitizer}}
-          cache-path: mfem/build/tests/unit/${{env.unit_tests}}
-      - uses: actions/download-artifact@v4
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        with:
-          name: tests-${{inputs.par}}-${{inputs.sanitizer}}
-          path: mfem/build/tests/unit
-      - name: Split Unit Tests
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build/tests/unit
-        run: |
-          chmod 755 ${{env.unit_tests}}
-          ./${{env.unit_tests}} --list-test-names-only | tail -n +2 > list-test-names
-          shuf list-test-names -o list-test-names
-          split --verbose -n l/4 -d -a 1 list-test-names list-test-names-
-      - name: Cat Unit Tests ${{matrix.tag}}
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build/tests/unit
-        run: cat list-test-names-${{matrix.tag}}
-      - name: Run Unit Tests ${{matrix.tag}}
-        if: ${{steps.restore.outputs.cache-hit != 'true'}}
-        working-directory: mfem/build
-        run: |
-          ${{env.CTEST}} tests/unit -R "${{env.unit_tests}}${{env.np}}" --show-only
-          ${{env.CTEST}} tests/unit -R "${{env.unit_tests}}${{env.np}}"
@@ -1,73 +0,0 @@
-# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
-# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
-# LICENSE and NOTICE for details. LLNL-CODE-806117.
-#
-# This file is part of the MFEM library. For more information and source code
-# availability visit https://mfem.org.
-#
-# MFEM is free software; you can redistribute it and/or modify it under the
-# terms of the BSD-3 license. We welcome feedback and contributions, see file
-# CONTRIBUTING.md for details.
---
-name: Sanitizers
-
-permissions:
-  actions: write
-
-on:
-  push:
-    branches: ["master", "next"]
-  pull_request:
-  workflow_dispatch:
-
-concurrency:
-  group: ${{github.workflow}}-${{github.ref}}
-  cancel-in-progress: true
-
-jobs:
-
-  # Build steps for dependencies
-  build-hypre:
-    uses: ./.github/workflows/sanitize-build-hypre.yml
-
-  build-metis:
-    uses: ./.github/workflows/sanitize-build-metis.yml
-
-  build-lsan:
-    uses: ./.github/workflows/sanitize-build-lsan.yml
-
-  build-libcxx:
-    uses: ./.github/workflows/sanitize-build-libcxx.yml
-
-  # Serial sanitizers: asan, msan, ubsan
-  seq-asan:
-    needs: [build-libcxx]
-    uses: ./.github/workflows/sanitize-tests.yml
-    with:
-      sanitizer: asan
-
-  seq-msan:
-    needs: [build-libcxx]
-    uses: ./.github/workflows/sanitize-tests.yml
-    with:
-      sanitizer: msan
-
-  seq-ubsan:
-    needs: [build-libcxx]
-    uses: ./.github/workflows/sanitize-tests.yml
-    with:
-      sanitizer: ubsan
-
-  # Parallel sanitizers: asan, ubsan
-  par-asan:
-    needs: [build-libcxx, build-hypre, build-metis]
-    uses: ./.github/workflows/sanitize-tests.yml
-    with:
-      par: true
-      sanitizer: asan
-  par-ubsan:
-    needs: [build-libcxx, build-hypre, build-metis]
-    uses: ./.github/workflows/sanitize-tests.yml
-    with:
-      par: true
-      sanitizer: ubsan
@@ -29,47 +29,3 @@ jobs:
        operations-per-run: 500
        exempt-issue-labels: "bug,WIP,ready-for-review,in-review,in-next"
        exempt-pr-labels: "bug,WIP,ready-for-review,in-review,in-next"
-
-  # Stale action for PRs with "in-review" label.
-  stale-in-review-pr:
-
-    runs-on: ubuntu-latest
-    permissions:
-      issues: write
-      pull-requests: write
-      actions: write
-
-    steps:
-    - uses: actions/stale@v9
-      with:
-        repo-token: ${{ secrets.GITHUB_TOKEN }}
-        stale-pr-message: ':warning: This PR has been automatically marked as stale because it has not had any activity in the last 150 days. *If no activity occurs in the next 30 days, it will be automatically closed.* Thank you for your contributions.'
-        only-pr-labels: "in-review"
-        days-before-pr-stale: 150
-        days-before-pr-close: 30
-        days-before-issue-stale: -1
-        days-before-issue-close: -1
-        stale-pr-label: 'stale'
-        operations-per-run: 500
-
-  # Stale action for PRs with "WIP" label.
-  stale-wip-pr:
-
-    runs-on: ubuntu-latest
-    permissions:
-      issues: write
-      pull-requests: write
-      actions: write
-
-    steps:
-    - uses: actions/stale@v9
-      with:
-        repo-token: ${{ secrets.GITHUB_TOKEN }}
-        stale-pr-message: ':warning: This PR has been automatically marked as stale because it has not had any activity in the last 300 days. *If no activity occurs in the next 30 days, it will be automatically closed.* Thank you for your contributions.'
-        only-pr-labels: "WIP"
-        days-before-pr-stale: 300
-        days-before-pr-close: 30
-        days-before-issue-stale: -1
-        days-before-issue-close: -1
-        stale-pr-label: 'stale'
-        operations-per-run: 500
@@ -54,6 +54,15 @@ doc/warnings.log
 # Example and miniapp binaries and outputs

 examples/ex[0-9]
+examples/ex5-max
+examples/ex5-hdg
+examples/ex5p-hdg
+examples/ex5-heat
+examples/ex5-nguyen
+examples/ex5p-nguyen
+examples/ex5-plasma
+examples/ex5-aniso
+examples/ex5-scatter
 examples/ex[0-9]p
 examples/ex1[04-9]
 examples/ex1[0-9]p
@@ -67,7 +76,7 @@ examples/ex4[0-9]p
 examples/refined.mesh
 examples/displaced.mesh
 examples/mesh.*
-examples/ex5.mesh
+examples/ex5*.mesh
 examples/Example5*
 examples/ParaView
 examples/Example9*
@@ -77,6 +86,8 @@ examples/sphere_refined.*
 examples/sol.*
 examples/sol_u.*
 examples/sol_p.*
+examples/sol_q.*
+examples/sol_t.*
 examples/sol_r.*
 examples/sol_i.*
 examples/ex6p-checkpoint.*
@@ -90,7 +101,7 @@ examples/velocity.*
 examples/elastic_energy.*
 examples/mode_*
 examples/mode_deriv_*
-examples/ex5-p-*.bp
+examples/ex5*-p-*.bp
 examples/ex9-p-*.bp
 examples/ex12-p-*.bp
 examples/ex16-p-*.bp
@@ -201,20 +212,14 @@ examples/superlu/sol.*
 miniapps/adjoint/cvsRoberts_ASAi_dns
 miniapps/adjoint/adjoint_advection_diffusion

-miniapps/dfem/dfem-minimal-surface
-miniapps/dfem/dfem-minimal-surface-output
-
 miniapps/electromagnetics/volta
 miniapps/electromagnetics/tesla
 miniapps/electromagnetics/maxwell
 miniapps/electromagnetics/joule
-miniapps/electromagnetics/lorentz
 miniapps/electromagnetics/Volta-AMR*
 miniapps/electromagnetics/Tesla-AMR*
 miniapps/electromagnetics/Maxwell-Parallel*
-miniapps/electromagnetics/Joule_[0-9]*
-miniapps/electromagnetics/Lorentz_[0-9]*
-miniapps/electromagnetics/Lorentz.dat
+miniapps/electromagnetics/Joule_*

 miniapps/gslib/field-diff
 miniapps/gslib/field-interp
@@ -235,7 +240,6 @@ miniapps/meshing/fit-node-position
 miniapps/meshing/trimmer
 miniapps/meshing/reflector
 miniapps/meshing/ref321
-miniapps/meshing/mesh-bounding-boxes
 miniapps/meshing/mesh-optimizer
 miniapps/meshing/pmesh-optimizer
 miniapps/meshing/pmesh-fitting
@@ -266,13 +270,11 @@ miniapps/meshing/mesh.*
 miniapps/meshing/order.*
 miniapps/meshing/sol.*
 miniapps/meshing/refined.mesh
-miniapps/meshing/bounding-box*
-miniapps/meshing/jacobian-determinant*

 miniapps/mtop/parheat
-miniapps/mtop/ParHeat/*
+miniapps/mtop/ParHeat*
 miniapps/mtop/seqheat
-miniapps/mtop/SeqHeat/*
+miniapps/mtop/SeqHeat*

 miniapps/autodiff/paradiff
 miniapps/autodiff/seqadiff
@@ -280,7 +282,7 @@ miniapps/autodiff/seqtest
 miniapps/autodiff/par_example
 miniapps/autodiff/seq_example
 miniapps/autodiff/seq_test
-miniapps/autodiff/Example/*
+miniapps/autodiff/Exampl*

 miniapps/navier/navier_mms
 miniapps/navier/navier_kovasznay
@@ -303,7 +305,6 @@ miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
-miniapps/nurbs/nurbs_surface
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
 miniapps/nurbs/sol_?.gf
@@ -322,7 +323,6 @@ miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
 miniapps/nurbs/glvis_naca-cmesh.mesh
 miniapps/nurbs/Naca_cmesh
-miniapps/nurbs/*-Surface.mesh

 miniapps/performance/ex1
 miniapps/performance/ex1p
@@ -344,7 +344,6 @@ miniapps/shifted/lsf_integral
 miniapps/tools/display-basis
 miniapps/tools/load-dc
 miniapps/tools/convert-dc
-miniapps/tools/gridfunction-bounds
 miniapps/tools/lor-transfer
 miniapps/tools/plor-transfer
 miniapps/tools/get-values
@@ -411,15 +410,12 @@ miniapps/spde/ParaView

 miniapps/tribol/contact-patch-test

-miniapps/diag-smoothers/abs-l1-jacobi
-miniapps/diag-smoothers/mg-abs-l1-jacobi
-
 # Unit test binary and outputs
 tests/unit/output_meshes
 tests/unit/unit_tests
 tests/unit/punit_tests
-tests/unit/gpu_unit_tests
-tests/unit/pgpu_unit_tests
+tests/unit/cunit_tests
+tests/unit/pcunit_tests
 tests/unit/sedov_tests_*
 tests/unit/psedov_tests_*
 tests/unit/tmop_pa_tests_*
@@ -22,7 +22,7 @@ include:
 # the "needs" keyword and express the DAG of jobs for more efficiency.
 # - We use setup and setup_baseline phases to download content outside of mfem
 #   directory.
-# - Allocate/Release is where Dane resource are allocated/released once for all.
+# - Allocate/Release is where ruby resource are allocated/released once for all.
 # - Build and Test is where we build and MFEM for multiple toolchains.
 # - Baseline_checks gathers baseline-type test suites execution
 # - Baseline_publish, only available on master, allows to update baseline
@@ -53,7 +53,7 @@ variables:
  AUTOTEST_COMMIT: "YES"

 # Trigger subpipelines:
-dane-build-and-test:
+ruby-build-and-test:
  stage: sub-pipelines
  variables:
    # Explicitly pass down values that we want to be able to set when triggering
@@ -61,10 +61,10 @@ dane-build-and-test:
    AUTOTEST: "${AUTOTEST}"
    AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
  trigger:
-    include: .gitlab/dane-build-and-test.yml
+    include: .gitlab/ruby-build-and-test.yml
    strategy: depend

-dane-baseline:
+ruby-baseline:
  stage: sub-pipelines
  variables:
    # Explicitly pass down values that we want to be able to set when triggering
@@ -73,7 +73,7 @@ dane-baseline:
    AUTOTEST: "${AUTOTEST}"
    AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
  trigger:
-    include: .gitlab/dane-baseline.yml
+    include: .gitlab/ruby-baseline.yml
    strategy: depend

 lassen-build-and-test:
@@ -24,7 +24,7 @@ and `test type`.

 Machines typically include:

-* Dane: Intel Sapphire Rapids
+* Ruby: 2nd Gen Intel Xeon (Cascade Lake)
 * Lassen: Power9 + Nvidia GPU
 * Corona: AMD GPU

@@ -76,13 +76,13 @@ with a spack spec of MFEM, within the limits permitted by the MFEM spack
 package.

 In any build-and-test sub-pipeline a job basically consists in defining the
-spack spec to use. Adding a job on Dane for example resumes to:
+spack spec to use. Adding a job on ruby for example resumes to:

 ```yaml
 <job_name>:
  variables:
    SPEC: "<spack_spec>"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby
 ```

 The remaining and non trivial work is to make sure this spec is working. To
@@ -24,7 +24,7 @@ variables:
 # TODO: add a clean-up mechanism
  BUILD_ROOT: ${USER_CI_TOP_DIR}/${CI_PROJECT_NAME}-${MACHINE_NAME}-pipeline-${CI_PIPELINE_ID}

-# On LLNL's Dane, there is only one allocation shared among jobs in order to
+# On LLNL's ruby, there is only one allocation shared among jobs in order to
 # save time and resource. This allocation has to be uniquely named so that we
 # are sure to retrieve it.
  ALLOC_NAME: ${CI_PROJECT_NAME}_ci_${CI_PIPELINE_ID}
@@ -9,17 +9,17 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-# GitLab pipelines configurations for the Dane machine at LLNL
+# GitLab pipelines configurations for the Ruby machine at LLNL
 variables:
-  MACHINE_NAME: dane
+  MACHINE_NAME: ruby

-.on_dane:
+.on_ruby:
  tags:
    - shell
-    - dane
+    - ruby
  rules:
-    # Don't run dane jobs if...
-    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_DANE == "OFF"'
+    # Don't run ruby jobs if...
+    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_RUBY == "OFF"'
      when: never
    # Don't run autotest update if...
    - if: '$CI_JOB_NAME =~ /report/ && $AUTOTEST != "YES"'
@@ -40,17 +40,16 @@ variables:
    - when: on_success

 # Spack helped builds
-# Generic dane build job, extending build script
-.build_and_test_on_dane:
-  extends: [.on_dane]
+# Generic ruby build job, extending build script
+.build_and_test_on_ruby:
+  extends: [.on_ruby]
  stage: build_and_test
  script:
    # THREADS is used by 'tests/gitlab/build_and_test', run below
-    # Dane has 224 threads/node and we run 7 separate jobs: 224=7*32
-    - export THREADS=28
+    - export THREADS=16
    - echo ${ALLOC_NAME}
    - export JOBID=$(squeue -h --name=${ALLOC_NAME} --format=%A)
    - echo ${JOBID}
    - echo ${MFEM_DATA_DIR}
    - echo ${SPEC}
-    - srun $( [[ -n "${JOBID}" ]] && echo "--jobid=${JOBID}" ) --reservation=ci -t 60 -N 1 tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data
+    - srun $( [[ -n "${JOBID}" ]] && echo "--jobid=${JOBID}" ) --reservation=ci -t 45 -N 1 tests/gitlab/build_and_test --spec "${SPEC}" --data-dir "${MFEM_DATA_DIR}" --data
@@ -18,7 +18,7 @@
 setup_baseline:
  tags:
    - shell
-    - dane
+    - ruby
  stage: setup
  variables:
    GIT_STRATEGY: none
@@ -16,7 +16,7 @@
 setup:
  tags:
    - shell
-    - dane
+    - ruby
  stage: setup
  variables:
    GIT_STRATEGY: none
@@ -19,8 +19,8 @@ stages:
  - cleanup
  - baseline_publish

-baselinecheck_mfem_intel_dane:
-  extends: [.on_dane]
+baselinecheck_mfem_intel_ruby:
+  extends: [.on_ruby]
  stage: baseline_check
  variables:
    # TPLS_DIR is used in .gitlab/scripts/baseline to provide the tpls location
@@ -31,8 +31,8 @@ baselinecheck_mfem_intel_dane:
  script:
    - echo ${BUILD_ROOT}
    - echo ${TPLS_DIR}
-    # Used by the tests in MFEM/tests, dane has 224 threads/node:
-    - export MFEM_TEST_NP=192
+    # Used by the tests in MFEM/tests:
+    - export MFEM_TEST_NP=48
    # The next script uses the following environment variables:
    # * BASELINE_TEST, SYS_TYPE, CI_PROJECT_DIR, ARTIFACTS_DIR,
    # * BUILD_ROOT, TPLS_DIR, MACHINE_NAME
@@ -44,7 +44,7 @@ baselinecheck_mfem_intel_dane:
  allow_failure: true

 cleanup:
-  extends: .on_dane
+  extends: .on_ruby
  stage: cleanup
  variables:
    GIT_STRATEGY: none
@@ -53,7 +53,7 @@ cleanup:
    - rm -rf "${BUILD_ROOT}" || true

 report_baseline:
-  extends: [.on_dane]
+  extends: [.on_ruby]
  stage: baseline_report
  script:
    - echo ${MACHINE_NAME}
@@ -113,8 +113,8 @@ report_baseline:
        exit $err
      ) 9> autotest.lock

-baselinepublish_mfem_dane:
-  extends: [.on_dane]
+baselinepublish_mfem_ruby:
+  extends: [.on_ruby]
  stage: baseline_publish
  rules:
    # - if: '$CI_COMMIT_BRANCH == "master" || $REBASELINE == "YES"'
@@ -129,5 +129,5 @@ baselinepublish_mfem_dane:

 include:
  - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/dane-config.yml
+  - local: .gitlab/configs/ruby-config.yml
  - local: .gitlab/configs/setup-baseline.yml
@@ -19,54 +19,54 @@ stages:
 allocate_resource:
  variables:
    GIT_STRATEGY: none
-  extends: .on_dane
+  extends: .on_ruby
  stage: allocate_resource
  script:
    - echo ${ALLOC_NAME}
    - salloc --exclusive --nodes=1 --reservation=ci --time=60 --no-shell --job-name=${ALLOC_NAME}
  timeout: 6h

-# GitLab jobs for the Dane machine at LLNL
+# GitLab jobs for the Ruby machine at LLNL
 debug_ser_gcc_10:
  variables:
    SPEC: "%gcc@10.3.1 +debug~mpi"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 debug_par_gcc_10:
  variables:
    SPEC: "%gcc@10.3.1 +debug+mpi"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 opt_ser_gcc_10:
  variables:
    SPEC: "%gcc@10.3.1 ~mpi"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 opt_par_gcc_10:
  variables:
    SPEC: "%gcc@10.3.1"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 opt_par_gcc_10_sundials:
  variables:
    SPEC: "%gcc@10.3.1 +sundials"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 opt_par_gcc_10_petsc:
  variables:
    SPEC: "%gcc@10.3.1 +petsc ^petsc+mumps~superlu-dist"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 opt_par_gcc_10_pumi:
  variables:
    SPEC: "%gcc@10.3.1 +pumi"
-  extends: .build_and_test_on_dane
+  extends: .build_and_test_on_ruby

 # Release
 release_resource:
  variables:
    GIT_STRATEGY: none
-  extends: .on_dane
+  extends: .on_ruby
  stage: release_resource_and_report
  script:
    - echo ${ALLOC_NAME}
@@ -78,17 +78,17 @@ release_resource:
 report_job_success:
  stage: release_resource_and_report
  extends:
-    - .on_dane
+    - .on_ruby
    - .report_job_success

 report_job_failure:
  stage: release_resource_and_report
  extends:
-    - .on_dane
+    - .on_ruby
    - .report_job_failure

 include:
  - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/dane-config.yml
+  - local: .gitlab/configs/ruby-config.yml
  - local: .gitlab/configs/setup-build-and-test.yml
  - local: .gitlab/configs/report-build-and-test.yml
@@ -14,7 +14,7 @@
 # locals
 glob_err=${BASELINE_TEST}.err
 base=${BASELINE_TEST}-${SYS_TYPE}
-if [[ "${MACHINE_NAME}" == "dane" ]]; then
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
  base="${BASELINE_TEST}-${MACHINE_NAME}"
 fi
 base_diff=${base}.diff
@@ -31,7 +31,7 @@ cd tests
 mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}

 # run
-if [[ "${MACHINE_NAME}" == "dane" ]]; then
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
  salloc --nodes=1 --exclusive --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
 elif [[ ${MACHINE_NAME} == "corona" ]]; then
  salloc --nodes=1 -t 60 -p pbatch ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
@@ -11,7 +11,7 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-# There will be collision between corona and dane baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 ARTIFACT_PATH=${CI_PROJECT_DIR}/${ARTIFACTS_DIR}/baseline-${SYS_TYPE}
@@ -21,7 +21,7 @@ PATCH_FILE=${ARTIFACT_PATH}.patch
 FULL_FILE=${ARTIFACT_PATH}.out
 DIFF_FILE=${ARTIFACT_PATH}.diff

-# There will be collision between corona and dane baselines.
+# There will be collision between corona and ruby baselines.
 # Once the corresponding files have been generated, we can switch to machine
 # specific ref.
 SAVED_NAME=baseline-${SYS_TYPE}.saved
@@ -8,124 +8,6 @@
                               https://mfem.org


-Version 4.8.1 (development)
-===========================
-
-Starting with this version, MFEM requires a C++17 compiler.
-
-Discretization improvements
---------------------------
- Introduced dFEM: a new MFEM capability for Automatic Differentiation (AD) of
-  nonlinear finite element operators, based on Enzyme or dual numbers AD at
-  quadrature points. These features are part of the new mfem::future namespace
-  and some of the API can change in the future. See the new dFEM minimal surface
-  miniapp in the miniapps/dfem/ directory for illustration of dFEM's use.
-
- Using Enzyme for AD in MFEM is tested with clang v19 and requires clang/LLVM
-  built with plugin support. See INSTALL for more details.
-
- In the ParMoonolith integration, added support for variational resampling of
-  H1 vector fields.
-
- Added support for boundary integration to the hyperbolic framework. In this
-  regard, new classes `BdrHyperbolicDirichletIntegrator` and
-  `BoundaryHyperbolicFlowIntegrator` have been introduced for implementation
-  of weak Dirichlet boundary conditions with a general flux or for the linear
-  case respectively.
-
- Added method to compute piecewise linear bounds on high-order functions on
-  tensor-product elements.
-
- Parallel anisotropic refinement of hexahedral meshes is now supported,
-  provided that neighboring hexahedra are not refined in conflicting directions.
-  A new ParMesh method is added to check for such conflicts, before refinement.
-
-Meshing improvements
--------------------
-
- Introduced NC-patch NURBS meshes, which are conforming element-wise but allow
-  for nonconforming patch topology. This new mesh format supports element
-  spacing formulas for refinement, as well as local refinement factors for a
-  subset of knot vectors.
-
- Added support for higher order meshes in Mesh::MakeSimplicial and
-  ParMesh::MakeSimplicial.
-
- Added a new miniapp for interpolating a surface grid of points in 3D using a
-  smooth NURBS surface, that can then be sampled at arbitrary resolution while
-  staying close to the original geometry. See miniapps/nurbs/nurbs_surface.
-
-GPU computing
-------------
- The function Vector::SetSubVector(const Array<int> &, const real_t) now
-  executes on device if either the vector or the array have the device flag
-  set. This is most often used for setting constant essential boundary
-  conditions. A new function Vector::SetSubVectorHost has been added in cases
-  where host execution is always needed (e.g. when the DOFs array is small).
-
- Introduced MFEM_FOREACH_THREAD_DIRECT, which directly maps loop tasks to GPU
-  threads, assigning one task per thread.
-
- Implemented a GPU-accelerated matrix-free AMR derefinement `GridFunction`
-  update operator. This supports mixed geometry meshes and variable order
-  spaces, and is the default derefinement operator constructed by
-  `FiniteElementSpace::Update` and `ParFiniteElementSpace::Update`.
-  The operator requires `FiniteElementSpace::Nonconforming() == true`.
- Added new method: GridFunction::GetGradients, with GPU support, for computing
-  the gradients of a GridFunction on all elements.
- Added GPU support in GradientGridFunctionCoefficient and
-  InnerProductCoefficient by implementing their Project methods.
-
-New and updated examples and miniapps
-------------------------------------
- Added miniapps to demonstrate an implementation of the absolute-value
-  L(1)-Jacobi preconditioners in partially assembled operators. This includes
-  Multigrid wrapper to demonstrate the effectiveness of these Jacobi-type
-  operators as smoothers.
-  These miniapps can be found in `miniapps/diag-smoothers`.
-
- Added a new miniapp (meshing/mesh-bounding-boxes) that computes the bounding
-  boxes for each element of a given mesh, and the bounds on the determinant of
-  the Jacobian of the transformation.
-
- Added a new miniapp (tools/gridfunction-bounds) to compute piecewise linear
-  bounds on a given high-order grid function.
-
- Added a new miniapp (electromagnetics/lorentz) which computes the trajectory
-  of a charged particle, subject to Lorentz forces, in electrostatic and/or
-  magnetostatic fields as computed by the volta or tesla miniapps.
-
-API changes:
-----------
- mfem::internal::tensor and mfem::internal::dual have been moved to
-  mfem::future::tensor and mfem::future::dual.
-
- API addition: in class `Operator`, added virtual functions: `AbsMult`, and
-  `AbsMultTranspose`; in class `Vector`, added `Abs` and `Pow`.
-
-Miscellaneous
-------------
- Added the "gpu", "raja-gpu", and "ceed-gpu" backend aliases/shortcuts which
-  automatically select between CUDA or HIP.
-
- The CUDA-specific names used by some of the unit tests like 'cunit_tests' and
-  'pcunit_tests' were replaced by names using 'gpu' instead of 'c' (short for
-  CUDA) or 'cuda'. These tests automatically run the CUDA/HIP tests based on the
-  MFEM build configuration.
-
- Added the option to enable GPU-aware MPI in MFEM using the environment
-  variable 'MFEM_GPU_AWARE_MPI' set to any value. Setting this environment
-  variable is an alternative to calling 'Device::SetGPUAwareMPI(true)'.
-
- Added parallel Address Sanitizer, serial and parallel Undefined Behavior
-  Sanitizer and serial Memory Sanitizer GitHub actions tests on Ubuntu.
-
- FindPointsGSLIB has a new constructor that accepts the mesh object and
-  internally calls the Setup() method so that the user does not have to.
-  The FreeData() method has also been moved to the destructor so the user does
-  not need to manually free-up the memory if the destructor is called before
-  MPI_Finalize().
-
 Version 4.8, released on Apr 9, 2025
 ====================================

@@ -18,8 +18,8 @@ message(STATUS "CMake version: ${CMAKE_VERSION}")
 set(USER_CONFIG "${CMAKE_CURRENT_SOURCE_DIR}/config/user.cmake" CACHE PATH
  "Path to optional user configuration file.")

-# Require C++17 and disable compiler-specific extensions
-set(CMAKE_CXX_STANDARD 17 CACHE STRING "C++ standard to use.")
+# Require C++11 and disable compiler-specific extensions
+set(CMAKE_CXX_STANDARD 11 CACHE STRING "C++ standard to use.")
 set(CMAKE_CXX_STANDARD_REQUIRED ON CACHE BOOL
  "Force the use of the chosen C++ standard.")
 set(CMAKE_CXX_EXTENSIONS OFF CACHE BOOL "Enable C++ standard extensions.")
@@ -59,7 +59,7 @@ project(mfem NONE)
 # Current version of MFEM, see also `makefile`.
 #   mfem_VERSION = (string)
 #   MFEM_VERSION = (int)   [automatically derived from mfem_VERSION]
-set(${PROJECT_NAME}_VERSION 4.8.1)
+set(${PROJECT_NAME}_VERSION 4.8.0)

 # Prohibit in-source build
 if (${PROJECT_SOURCE_DIR} STREQUAL ${PROJECT_BINARY_DIR})
@@ -133,6 +133,7 @@ if (MFEM_USE_CUDA)
   if (NOT CMAKE_CUDA_HOST_COMPILER)
      set(CMAKE_CUDA_HOST_COMPILER ${CMAKE_CXX_COMPILER})
   endif()
+   set(CUDA_FLAGS "--expt-extended-lambda")
   if (CMAKE_VERSION VERSION_LESS 3.18.0)
      set(CUDA_FLAGS "-arch=${CUDA_ARCH} ${CUDA_FLAGS}")
   elseif (NOT CMAKE_CUDA_ARCHITECTURES)
@@ -147,20 +148,6 @@ if (MFEM_USE_CUDA)
   endif()
   message(STATUS "Using CUDA architecture: ${CUDA_ARCH}")
   enable_language(CUDA)
-   if (CMAKE_VERSION VERSION_LESS 3.18.0)
-     # backup try to detect if this is clang or nvcc
-     if(CMAKE_CUDA_COMPILER MATCHES "nvcc$")
-       # nvcc
-       set(MFEM_CUDA_COMPILER_IS_NVCC ON)
-       set(CUDA_FLAGS "${CUDA_FLAGS} --expt-extended-lambda --expt-relaxed-constexpr")
-     endif()
-   else()
-     if (CMAKE_CUDA_COMPILER_ID STREQUAL "NVIDIA")
-       # nvcc
-       set(MFEM_CUDA_COMPILER_IS_NVCC ON)
-       set(CUDA_FLAGS "${CUDA_FLAGS} --expt-extended-lambda --expt-relaxed-constexpr")
-     endif()
-   endif()
   set(CMAKE_CUDA_STANDARD ${CMAKE_CXX_STANDARD} CACHE STRING
      "CUDA standard to use.")
   set(CMAKE_CUDA_STANDARD_REQUIRED ON CACHE BOOL
@@ -269,20 +256,11 @@ if (MFEM_USE_OPENMP OR MFEM_USE_LEGACY_OPENMP)
  if (OPENMP_FOUND)
    set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
    if (MFEM_USE_CUDA)
-      if(MFEM_CUDA_COMPILER_IS_NVCC)
-        set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} -Xcompiler=${OpenMP_CXX_FLAGS}")
-      else()
-        set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} ${OpenMP_CXX_FLAGS}")
-      endif()
+      set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} -Xcompiler=${OpenMP_CXX_FLAGS}")
    endif()
  endif()
 endif()

-# Umpire (must be included before hypre, so hypre can use it if needed)
-if (MFEM_USE_UMPIRE)
-   find_package(UMPIRE REQUIRED)
-endif()
-
 # MPI -> hypre; PETSc (optional)
 if (MFEM_USE_MPI)
  find_package(MPI REQUIRED)
@@ -410,11 +388,6 @@ if (MFEM_USE_GSLIB)
  find_package(GSLIB REQUIRED)
 endif()

-# HDF5
-if (MFEM_USE_HDF5)
-  find_package(HDF5 REQUIRED)
-endif()
-
 # NetCDF
 if (MFEM_USE_NETCDF)
  find_package(NetCDF REQUIRED)
@@ -500,13 +473,14 @@ endif()

 # RAJA
 if (MFEM_USE_RAJA)
-   # RAJA uses FindCUDA, which needs CMP0146=OLD in CMake >= 3.27
-   if(CMAKE_VERSION VERSION_GREATER_EQUAL 3.27.0)
-      cmake_policy(SET CMP0146 OLD)
-   endif()
   find_package(RAJA REQUIRED)
 endif()

+# UMPIRE
+if (MFEM_USE_UMPIRE)
+   find_package(UMPIRE REQUIRED)
+endif()
+
 # GOOGLE-BENCHMARK
 if (MFEM_USE_BENCHMARK)
   find_package(Benchmark REQUIRED)
@@ -553,10 +527,9 @@ if (MFEM_USE_TRIBOL)
  endif()
 endif()

+# Enzyme
 if (MFEM_USE_ENZYME)
-    find_package(Enzyme REQUIRED HINTS ${ENZYME_DIR})
-    message(STATUS "Enzyme found in ${ENZYME_DIR}.")
-    set(ENZYME_INCLUDE_DIRS ${ENZYME_DIR}/include)
+   find_package(ENZYME REQUIRED)
 endif()

 # MFEM_TIMER_TYPE
@@ -596,29 +569,22 @@ find_package(Threads REQUIRED)
 #    integers, the METIS header (with 32-bit indices, as used by mfem) needs to
 #    be before SuiteSparse.
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
-    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB HDF5
+    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
    NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
    ADIOS2 MKL_CPARDISO MKL_PARDISO AMGX MAGMA CUSPARSE CUBLAS CALIPER CODIPACK
    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPBLAS HIPSPARSE MOONOLITH BLITZ
-    ALGOIM ENZYME CUDA::cudart)
+    ALGOIM ENZYME)

-# Add all created targets and *_FOUND libraries in the variables TPL_TARGETS and
-# TPL_LIBRARIES, respectively.
-set(TPL_TARGETS)
+# Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
 set(TPL_INCLUDE_DIRS "")
 foreach(TPL IN LISTS MFEM_TPLS)
-  if (${TPL}_FOUND OR TARGET ${TPL})
+  if (${TPL}_FOUND)
    message(STATUS "MFEM: using package ${TPL}")
-    if (TARGET ${TPL})
-      list(APPEND TPL_TARGETS ${TPL})
-    else()
-      list(APPEND TPL_LIBRARIES ${${TPL}_LIBRARIES})
-      list(APPEND TPL_INCLUDE_DIRS ${${TPL}_INCLUDE_DIRS})
-    endif()
+    list(APPEND TPL_LIBRARIES ${${TPL}_LIBRARIES})
+    list(APPEND TPL_INCLUDE_DIRS ${${TPL}_INCLUDE_DIRS})
  endif()
 endforeach(TPL)
-
 list(REVERSE TPL_LIBRARIES)
 list(REMOVE_DUPLICATES TPL_LIBRARIES)
 list(REVERSE TPL_LIBRARIES)
@@ -691,10 +657,7 @@ set(MFEM_INSTALL_DIR ${CMAKE_INSTALL_PREFIX})
 # Declaring the library
 mfem_add_library(mfem ${SOURCES} ${HEADERS} ${MASTER_HEADERS})
 # message(STATUS "TPL_LIBRARIES = ${TPL_LIBRARIES}")
-target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES} ${TPL_TARGETS})
-if (TPL_TARGETS)
-  add_dependencies(mfem ${TPL_TARGETS})
-endif()
+target_link_libraries(mfem PUBLIC ${TPL_LIBRARIES})
 if (MINGW)
  target_link_libraries(mfem PRIVATE ws2_32)
 endif()
@@ -718,9 +681,6 @@ if (MFEM_USE_MPI)
    target_link_libraries(mfem PUBLIC ${MPI_CXX_LINK_FLAGS})
  endif()
 endif()
-if (MFEM_USE_ENZYME)
-  target_link_libraries(mfem PUBLIC ClangEnzymeFlags)
-endif()

 set_target_properties(mfem PROPERTIES VERSION "${mfem_VERSION}")
 set_target_properties(mfem PROPERTIES SOVERSION "${mfem_VERSION}")
@@ -120,7 +120,6 @@ The MFEM source code has the following structure:
  |   └── superlu
  ├── fem
  │   ├── ceed
-  │   ├── dfem
  │   ├── eltrans
  │   ├── fe
  │   ├── gslib
@@ -139,7 +138,6 @@ The MFEM source code has the following structure:
  │   ├── adjoint
  │   ├── autodiff
  │   ├── common
-  │   ├── dfem
  │   ├── dpg
  │   ├── electromagnetics
  │   ├── gslib
@@ -551,8 +549,6 @@ Before a PR can be merged, it should satisfy the following:
      - [ ] Add a short description of the example in the "Extensive Examples" section of `features.md`.
 - [ ] New miniapps:
   - [ ] All sample runs at the top of the miniapp source file work.
-   - [ ] Add to internal testing repo, if sample runs should be included in nightly tests [internally](#tests-at-llnl).
-   - [ ] Exclude long sample runs from automated testing, with `* ` (one space) before the command.
   - [ ] Update top-level `makefile` and `makefile` in corresponding miniapp directory.
   - [ ] Add the miniapp binary and any files generated by it to the top-level `.gitignore` file.
   - [ ] Update CMake build system:
@@ -747,7 +743,7 @@ and debug build is performed with a simple run of `ex1` to verify the executable
 - We mirror the `master` and `next` branches internally (to `gh-master` and
  `gh-next`) and run longer nightly tests via cron. On the weekends, a more
  extensive test is run which extracts and executes all the different sample
-  runs from each example and most miniapps.
+  runs from each example.

 - We also mirror PRs on the LLNL GitLab instance. PR mirroring can only be
  triggered by _LLNL developers_, but test status is publicly available. Only
@@ -121,11 +121,6 @@ Parallel build:
   make -j 4
 (For METIS 5, see https://mfem.org/building/#parallel-build-using-metis-5)

-Parallel build with fetching of hypre and METIS:
-   mkdir <mfem-buil-dir> ; cd <mfem-build-dir>
-   cmake <mfem-source-dir> -DMFEM_USE_MPI=YES -DFETCH_TPLS=YES
-   make -j 4
-
 CUDA build:
   (this build requires CMake 3.17 or newer)
   mkdir <mfem-build-dir> ; cd <mfem-build-dir>
@@ -268,7 +263,7 @@ See the configuration file config/defaults.mk for the default settings.
 Compilers:
   CXX      - C++ compiler, serial build
   MPICXX   - MPI C++ compiler, parallel build
-   CUDA_CXX - The CUDA compiler, 'nvcc' or 'clang++'
+   CUDA_CXX - The CUDA compiler, 'nvcc'

 Compiler options:
   OPTIM_FLAGS - Options for optimized build
@@ -428,10 +423,6 @@ MFEM_USE_GNUTLS = YES/NO
   When MFEM_USE_GNUTLS is enabled, the additional build options, GNUTLS_*, are
   also used, see below.

-MFEM_USE_HDF5 = YES/NO
-   The HDF5 library is used for input and output of HDF5 files, for example
-   Cubit mesh files or VTKHDF files for ParaView.
-
 MFEM_USE_NETCDF = YES/NO
   NetCDF is the library that is used by the SNL Cubit mesh generator to create
   Genesis mesh files. This option enables a reader for these files, which
@@ -613,12 +604,11 @@ MFEM_USE_TRIBOL = YES/NO

 MFEM_USE_ENZYME = YES/NO
   Enables automatic differentiation support through the LLVM plugin Enzyme.
-   This requires the compiler to be set to clang (>=14.0.0). We also advise the
-   use of the link time optimization (LTO) plugin, so functions defined over
-   multiple files (compilation units) can be differentiated automatically. This
-   requires to also use LLVM/LLD for linking. The recommended options are in
-   config/defaults.mk. For more detailed instructions, see the section "Specific
-   options for Enzyme" below.
+   This requires the compiler to be set to clang (>=14.0.0). We also advise to
+   use the link time optimization (LTO) plugin, to enable functions that you
+   define over multiple files (compilation units) and want to be differentiated
+   automatically, to work. This requires to also use LLVM/LLD for linking.
+   Recommended options are in config/defaults.mk.

 MFEM_BUILD_TAG = (any value)
   An optional tag to characterize the build. Exported to config/config.mk.
@@ -668,7 +658,6 @@ The specific libraries and their options are:
 - OpenMP (optional), usually part of compiler, used when either MFEM_USE_OPENMP
  or MFEM_USE_LEGACY_OPENMP is set to YES.
  Options: OPENMP_OPT, OPENMP_LIB.
-  Versions: OpenMP >= 3.1 when MFEM_USE_OPENMP=YES.

 - High-resolution POSIX clocks: when using MFEM_TIMER_TYPE = 2, it may be
  necessary to link with a system library (e.g. librt.so).
@@ -744,9 +733,6 @@ The specific libraries and their options are:
  Options: GNUTLS_OPT, GNUTLS_LIB.
  Versions: GnuTLS >= 2.12.0, older versions may work too.

- HDF5 (optional), used when MFEM_USE_HDF5 = YES, required for reading and
-  writing files in VTKHDF format.
-
 - NetCDF (optional), used when MFEM_USE_NETCDF = YES, required for reading Cubit
  mesh files. Also requires installation of HDF5 and ZLIB, as explained at the
  NetCDF web site. Note that we use the plain vanilla "C" version of NetCDF, you
@@ -842,13 +828,12 @@ The specific libraries and their options are:

 - CUDA (optional), used when MFEM_USE_CUDA = YES.
  URL: https://developer.nvidia.com/cuda-toolkit
-  Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB, CUDA_DIR (when CUDA_CXX=clang++).
+  Options: CUDA_CXX, CUDA_ARCH, CUDA_OPT, CUDA_LIB.
  Versions: CUDA >= 10.1.168.

 - HIP (optional), used when MFEM_USE_HIP = YES.
  URL: https://rocmdocs.amd.com
  Options: HIP_CXX, HIP_ARCH, HIP_OPT, HIP_LIB.
-  Versions: ROCm >= 5.6.1.

 - OCCA (optional), used when MFEM_USE_OCCA = YES.
  URL: https://libocca.org
@@ -859,7 +844,7 @@ The specific libraries and their options are:
  URL: https://github.com/CEED/libCEED
       https://ceed.exascaleproject.org/libceed
  Options: CEED_DIR, CEED_OPT, CEED_LIB.
-  Versions: libCEED >= 0.12.0.
+  Versions: libCEED >= 0.12.

 - RAJA (optional), used when MFEM_USE_RAJA = YES.
  Beginning with MFEM v4.5.1, only RAJA v2022.10.3+ is supported.
@@ -919,7 +904,7 @@ The specific libraries and their options are:
 - Enzyme, used when MFEM_USE_ENZYME = YES. Requires LLVM/Clang >= 14.0.0.
  URL: https://github.com/EnzymeAD/Enzyme
  Options: ENZYME_DIR, ENZYME_OPT, ENZYME_LIB.
-  Versions: Enzyme >= v0.0.176.
+  Versions: Enzyme >= v0.0.33.


 Building with CMake
@@ -1053,7 +1038,6 @@ MFEM_USE_STRUMPACK
 MFEM_USE_GINKGO
 MFEM_USE_AMGX
 MFEM_USE_GNUTLS
-MFEM_USE_HDF5
 MFEM_USE_NETCDF
 MFEM_USE_MPFR
 MFEM_USE_ZLIB
@@ -1081,9 +1065,6 @@ The following options are CMake specific:
 MFEM_ENABLE_TESTING  - Enable the ctest framework for testing.
 MFEM_ENABLE_EXAMPLES - Build all of the examples by default.
 MFEM_ENABLE_MINIAPPS - Build all of the miniapps by default.
-FETCH_TPLS           - Enable fetching of all supported third-party libraries.
-HYPRE_FETCH          - Enable fetching of hypre.
-METIS_FETCH          - Enable fetching of metis.

 External libraries (CMake):
 ---------------------------
@@ -1145,12 +1126,6 @@ The following built-in CMake packages are also used:
      set the <LIBNAME>_LIBRARIES option directly; the configuration option
      <LIBNAME>_DIR is not supported.

-The MFEM CMake build system also provides fetching (automated building) for the
-packages/libraries listed below. Note that when fetching is enabled, any related
-auto-detection functionality is disabled.
-
- - HYPRE
- - METIS

 Building without GNU make or CMake
 ==================================
@@ -1207,73 +1182,3 @@ the older HIP C++ library build/linkage. To ensure proper build and linkage
 check that `CMAKE_CXX_COMPILER` and `CMAKE_HIP_COMPILER` are set to the same
 compiler. This is especially important when using an MPI compiler (for example
 crayCC) where some linker flags may get dropped if these two are not identical.
-
-Specific options for Enzyme
-===========================
-To work properly, MFEM and Enzyme need to use the same LLVM/Clang configuration.
-For example, on macOS this can be done by using Homebrew: first install Enzyme,
-which in turn installs LLVM as a dependency (as of May 2025, this is LLVM 19):
-
-   brew install enzyme
-
-In order to ensure the correct compiler choice for the MFEM makefile build, set
-
-   CXX = $(shell brew --prefix llvm@19)/bin/clang++
-
-in the user.mk file (adapted from config/defaults.mk, see the section "Building
-with GNU make" above). With MPI, it is convenient to set
-
-   MPICXX = OMPI_CXX=$(CXX) mpicxx
-
-for OpenMPI and
-
-   MPICXX = MPICH_CXX=$(CXX) mpicxx
-
-for MPICH.
-
-Additionally, the Enzyme directory needs to be set in user.mk as follows:
-
-   ENZYME_DIR = $(shell brew --prefix enzyme)
-
-Specifically, a full build on a Mac can be tested by adding the following
-user.mk file in the config/ directory
-
-   MFEM_USE_ENZYME = YES
-   ENZYME_DIR = $(shell brew --prefix enzyme)
-   LLVM_DIR = $(shell brew --prefix llvm@19)
-   CXX = $(LLVM_DIR)/bin/clang++
-   MFEM_USE_MPI = YES
-   MPICXX = OMPI_CXX=$(CXX) mpicxx
-
-and running
-
-   make config
-   make -j
-   cd miniapps/dfem
-   make
-   ./dfem-minimal-surface
-
-On Linux systems, for example Ubuntu 24.04, use the package manager to install
-the Enzyme dependencies
-
-   sudo apt install libclang-dev libzstd-dev llvm-dev clang
-
-and then clone and build Enzyme
-
-   cd $HOME
-   git clone https://github.com/EnzymeAD/Enzyme.git
-   cd Enzyme/enzyme && mkdir build && cd build
-   CC=clang CXX=clang++ cmake .. -DLLVM_DIR=/usr/lib/llvm-18/lib/cmake -DCMAKE_INSTALL_PREFIX=$HOME/Enzyme/enzyme/build
-   make -j
-   make install
-
-From here, one can proceed in the same way using the following user.mk settings
-
-   MFEM_USE_ENZYME = YES
-   ENZYME_DIR = $(HOME)/Enzyme/enzyme/build
-   CXX = clang++
-   MFEM_USE_MPI = YES
-   MPICXX = OMPI_CXX=$(CXX) mpicxx
-
-On other Linux systems the LLVM packages may have different names, for example
-on RHEL9, one needs to "sudo yum install llvm-devel libzstd clang-devel".
@@ -41,7 +41,6 @@ set(MFEM_USE_MAGMA @MFEM_USE_MAGMA@)
 set(MFEM_USE_HIOP @MFEM_USE_HIOP@)
 set(MFEM_USE_GNUTLS @MFEM_USE_GNUTLS@)
 set(MFEM_USE_GSLIB @MFEM_USE_GSLIB@)
-set(MFEM_USE_HDF5 @MFEM_USE_HDF5@)
 set(MFEM_USE_NETCDF @MFEM_USE_NETCDF@)
 set(MFEM_USE_PETSC @MFEM_USE_PETSC@)
 set(MFEM_USE_SLEPC @MFEM_USE_SLEPC@)
@@ -84,31 +83,6 @@ set_and_check(MFEM_LIBRARY_DIR "@PACKAGE_LIB_INSTALL_DIR@")

 check_required_components(MFEM)

-include(CMakeFindDependencyMacro)
-
-if (MFEM_USE_CUDA)
-  # required for projects linking to MFEM+CUDA, even if they don't use CUDA directly
-  find_dependency(CUDAToolkit)
-endif (MFEM_USE_CUDA)
-
-if (MFEM_USE_HIP)
-  # hip/rocm uses the modern MFEM way of linking to targets, need to find dependencies
-  find_dependency(HIP)
-  find_dependency(HIPBLAS)
-  find_dependency(HIPSPARSE)
-  if (MFEM_USE_MPI)
-    # assume HYPRE uses HIP
-    # alternatively could check HYPRE_USING_HIP
-    find_dependency(rocsparse)
-    find_dependency(rocrand)
-    find_dependency(rocsolver)
-  endif (MFEM_USE_MPI)
-endif (MFEM_USE_HIP)
-
-if (MFEM_USE_RAJA)
-   find_dependency(RAJA)
-endif()
-
 if (NOT TARGET mfem)
  include(${CMAKE_CURRENT_LIST_DIR}/MFEMTargets.cmake)
 endif (NOT TARGET mfem)
@@ -132,9 +132,6 @@
 // Enable Conduit support.
 #cmakedefine MFEM_USE_CONDUIT

-// Enable functionality based on the HDF5 library (reading VTKHDF files).
-#cmakedefine MFEM_USE_HDF5
-
 // Enable functionality based on the NetCDF library (reading CUBIT files).
 #cmakedefine MFEM_USE_NETCDF

@@ -0,0 +1,27 @@
+# Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
+# at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+# LICENSE and NOTICE for details. LLNL-CODE-806117.
+#
+# This file is part of the MFEM library. For more information and source code
+# availability visit https://mfem.org.
+#
+# MFEM is free software; you can redistribute it and/or modify it under the
+# terms of the BSD-3 license. We welcome feedback and contributions, see file
+# CONTRIBUTING.md for details.
+
+message(STATUS "Looking for ENZYME ...")
+message(STATUS "   in ENZYME_DIR = ${ENZYME_DIR}")
+
+# Make sure the directory and version combination works. Do nothing otherwise.
+if(EXISTS "${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
+  message(STATUS "Found ENZYME: ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so")
+
+  # Set ENZYME_FOUND
+  set(ENZYME_FOUND TRUE CACHE BOOL "ENZYME was found." FORCE)
+
+  # Set CXX flags to accommodate the Enzyme Clang plugin
+  set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Xclang -load -Xclang ${ENZYME_DIR}/ClangEnzyme-${ENZYME_VERSION}.so -mllvm -enzyme-loose-types=1")
+  set(MFEM_USE_ENZYME YES)
+else()
+
+endif()
@@ -9,25 +9,21 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-# Defines the following variables if fetching of TPLs is disabled (default):
+# Defines the following variables:
 #   - HYPRE_FOUND
 #   - HYPRE_LIBRARIES
 #   - HYPRE_INCLUDE_DIRS
 #   - HYPRE_VERSION
 #   - HYPRE_USING_CUDA (internal)
 #   - HYPRE_USING_HIP (internal)
-# otherwise, the following are defined:
-#   - HYPRE (imported library target)
-#   - HYPRE_VERSION (cache variable)

-if (HYPRE_FOUND OR TARGET HYPRE)
+if (HYPRE_FOUND)
  if (HYPRE_USING_CUDA)
    find_package(CUDAToolkit REQUIRED)
  endif()
  if (HYPRE_USING_HIP)
    find_package(rocsparse REQUIRED)
    find_package(rocrand REQUIRED)
-    find_package(rocsolver REQUIRED)
  endif()
  if (HYPRE_LIBRARIES AND HYPRE_INCLUDE_DIRS AND HYPRE_VERSION)
    find_package_handle_standard_args(HYPRE
@@ -37,95 +33,6 @@ if (HYPRE_FOUND OR TARGET HYPRE)
  endif()
 endif()

-if (HYPRE_FETCH OR FETCH_TPLS)
-  # Collect all HYPRE_ENABLE variables and pass them to hypre, assuming they are BOOL.
-  set(HYPRE_CMAKE_OPTIONS "")
-  get_cmake_property(all_vars VARIABLES)
-  foreach(var ${all_vars})
-    if(var MATCHES "^HYPRE_ENABLE")
-      list(APPEND HYPRE_CMAKE_OPTIONS "-D${var}:BOOL=${${var}}")
-    endif()
-  endforeach()
-
-  set(HYPRE_FETCH_VERSION 2.33.0)
-  set(HYPRE_FETCH_TAG "v${HYPRE_FETCH_VERSION}" CACHE STRING "Tag, branch, or commit for HYPRE")
-  add_library(HYPRE STATIC IMPORTED)
-  # set options and associated dependencies
-  list(APPEND HYPRE_CMAKE_OPTIONS -DCMAKE_BUILD_TYPE:STRING=${CMAKE_BUILD_TYPE})
-  if (MFEM_USE_CUDA)
-    list(APPEND HYPRE_CMAKE_OPTIONS -DHYPRE_ENABLE_CUDA:BOOL=ON -DCMAKE_CUDA_ARCHITECTURES:STRING=${CMAKE_CUDA_ARCHITECTURES})
-    find_package(CUDAToolkit REQUIRED)
-    target_link_libraries(HYPRE INTERFACE CUDA::cusparse CUDA::curand CUDA::cublas)
-  elseif (MFEM_USE_HIP)
-    list(APPEND HYPRE_CMAKE_OPTIONS -DHYPRE_ENABLE_HIP:BOOL=ON)
-    find_package(rocsparse REQUIRED)
-    find_package(rocrand REQUIRED)
-    target_link_libraries(HYPRE INTERFACE rocsparse rocrand)
-  endif()
-  if (MFEM_USE_CUDA OR MFEM_USE_HIP)
-    if (MFEM_USE_UMPIRE)
-      if (EXISTS ${umpire_DIR})
-        list(APPEND HYPRE_CMAKE_OPTIONS -DHYPRE_ENABLE_UMPIRE:BOOL=ON -Dumpire_DIR:PATH=${umpire_DIR})
-      else()
-        message(FATAL_ERROR "MFEM_USE_UMPIRE=ON, however umpire_DIR isn't visible to HYPRE")
-      endif()
-    else()
-      list(APPEND HYPRE_CMAKE_OPTIONS -DHYPRE_ENABLE_UMPIRE:BOOL=OFF)
-      message(WARNING
-"================================================================================
- Umpire is disabled while building HYPRE with GPU support.
- This is not recommended for performance reasons!
- Consider enabling Umpire with -DMFEM_USE_UMPIRE=ON and providing -DUMPIRE_DIR.
-================================================================================")
-    endif()
-  endif()
-  if (MFEM_USE_SINGLE)
-    list(APPEND HYPRE_CMAKE_OPTIONS -DHYPRE_ENABLE_SINGLE:BOOL=ON)
-  endif()
-  # define external project and create future include directory so it is present
-  # to pass CMake checks at end of MFEM configuration step
-  message(STATUS "Will fetch HYPRE ${HYPRE_FETCH_TAG} to be built with ${HYPRE_CMAKE_OPTIONS}")
-  set(HYPRE_INSTALL ${CMAKE_BINARY_DIR}/fetch/hypre)
-  include(ExternalProject)
-  ExternalProject_Add(hypre
-    GIT_REPOSITORY https://github.com/hypre-space/hypre.git
-    GIT_TAG ${HYPRE_FETCH_TAG}
-    GIT_SHALLOW TRUE
-    GIT_PROGRESS TRUE
-    UPDATE_DISCONNECTED TRUE
-    SOURCE_SUBDIR src
-    PREFIX ${HYPRE_INSTALL}
-    BUILD_COMMAND ${CMAKE_COMMAND} --build . -- -j${CMAKE_BUILD_PARALLEL_LEVEL}
-    CMAKE_CACHE_ARGS -DCMAKE_INSTALL_PREFIX:PATH=${HYPRE_INSTALL} -DCMAKE_INSTALL_LIBDIR:PATH=lib ${HYPRE_CMAKE_OPTIONS})
-  file(MAKE_DIRECTORY ${HYPRE_INSTALL}/include)
-  # set imported library target properties
-  add_dependencies(HYPRE hypre)
-  set_target_properties(HYPRE PROPERTIES
-    IMPORTED_LOCATION ${HYPRE_INSTALL}/lib/libHYPRE.a
-    INTERFACE_INCLUDE_DIRECTORIES ${HYPRE_INSTALL}/include)
-  # convert HYPRE version to integer
-  if (HYPRE_FETCH_TAG MATCHES "^v?([0-9]+)\\.([0-9]+)\\.([0-9]+)$")
-    # Exact release tag X.Y.Z
-    string(REGEX MATCHALL "[0-9]+" HYPRE_SPLIT_VERSION "${HYPRE_FETCH_TAG}")
-  elseif (HYPRE_FETCH_VERSION MATCHES "([0-9]+)\\.([0-9]+)(\\.([0-9]+))?")
-    string(REGEX MATCHALL "[0-9]+" HYPRE_SPLIT_VERSION "${HYPRE_FETCH_VERSION}")
-  else (NOT DEFINED HYPRE_VERSION)
-    message(FATAL_ERROR "Unable to find HYPRE release version. Please provide it via -DHYPRE_VERSION")
-  endif()
-  if (HYPRE_SPLIT_VERSION AND NOT DEFINED HYPRE_VERSION)
-    list(GET HYPRE_SPLIT_VERSION 0 HYPRE_MAJOR_VERSION)
-    list(GET HYPRE_SPLIT_VERSION 1 HYPRE_MINOR_VERSION)
-    if (HYPRE_SPLIT_VERSION GREATER 2)
-      list(GET HYPRE_SPLIT_VERSION 2 HYPRE_PATCH_VERSION)
-    else()
-      set(HYPRE_PATCH_VERSION 0)
-    endif()
-    math(EXPR HYPRE_VERSION "10000*${HYPRE_MAJOR_VERSION} + 100*${HYPRE_MINOR_VERSION} + ${HYPRE_PATCH_VERSION}")
-    set(HYPRE_VERSION ${HYPRE_VERSION} CACHE STRING "HYPRE version." FORCE)
-  endif()
-  return()
-endif()
-
 include(MfemCmakeUtilities)
 mfem_find_package(HYPRE HYPRE HYPRE_DIR "include" "HYPRE.h" "lib" "HYPRE"
  "Paths to headers required by HYPRE." "Libraries required by HYPRE."
@@ -179,9 +86,8 @@ if (HYPRE_FOUND AND HYPRE_USING_CUDA)
  mfem_culib_set_libraries(CUSPARSE cusparse)
  mfem_culib_set_libraries(CURAND curand)
  mfem_culib_set_libraries(CUBLAS cublas)
-  mfem_culib_set_libraries(CUSOLVER cusolver)
  list(APPEND HYPRE_LIBRARIES ${CUSPARSE_LIBRARIES} ${CURAND_LIBRARIES}
-       ${CUBLAS_LIBRARIES} ${CUSOLVER_LIBRARIES})
+       ${CUBLAS_LIBRARIES})
  set(HYPRE_LIBRARIES ${HYPRE_LIBRARIES} CACHE STRING
      "HYPRE libraries + dependencies." FORCE)
  message(STATUS "Updated HYPRE_LIBRARIES: ${HYPRE_LIBRARIES}")
@@ -190,8 +96,7 @@ endif()
 if (HYPRE_FOUND AND HYPRE_USING_HIP)
  find_package(rocsparse REQUIRED)
  find_package(rocrand REQUIRED)
-  find_package(rocsolver REQUIRED)
-  list(APPEND HYPRE_LIBRARIES ${rocsparse_LIBRARIES} ${rocrand_LIBRARIES} roc::rocsolver roc::rocblas)
+  list(APPEND HYPRE_LIBRARIES ${rocsparse_LIBRARIES} ${rocrand_LIBRARIES})
  set(HYPRE_LIBRARIES ${HYPRE_LIBRARIES} CACHE STRING
      "HYPRE libraries + dependencies." FORCE)
  message(STATUS "Updated HYPRE_LIBRARIES: ${HYPRE_LIBRARIES}")
@@ -9,39 +9,10 @@
 # terms of the BSD-3 license. We welcome feedback and contributions, see file
 # CONTRIBUTING.md for details.

-# Defines the following variables if fetching of TPLs is disabled (default):
+# Defines the following variables:
 #   - METIS_FOUND
 #   - METIS_LIBRARIES
 #   - METIS_INCLUDE_DIRS
-#   - METIS_VERSION_5
-# otherwise, the following are defined:
-#   - METIS (imported library target)
-#   - METIS_VERSION_5 (cache variable)
-
-if (METIS_FETCH OR FETCH_TPLS)
-  set(METIS_FETCH_VERSION 4.0.3)
-  add_library(METIS STATIC IMPORTED)
-  # define external project
-  message(STATUS "Will fetch METIS ${METIS_FETCH_VERSION} to be built with default options")
-  set(PREFIX ${CMAKE_BINARY_DIR}/fetch/metis)
-  include(ExternalProject)
-  ExternalProject_Add(metis
-    GIT_REPOSITORY https://github.com/mfem/tpls
-    GIT_TAG b60352fbe9675d374b00828055e55be4584c7995 # tag from 1/16/25
-    GIT_SHALLOW TRUE
-    UPDATE_DISCONNECTED TRUE
-    PREFIX ${PREFIX}
-    CONFIGURE_COMMAND tar -xzf ../metis/metis-${METIS_FETCH_VERSION}-mac.tgz --strip=1
-    BUILD_COMMAND $(MAKE) COPTIONS=-Wno-incompatible-pointer-types
-    INSTALL_COMMAND mkdir -p ${PREFIX}/lib && cp libmetis.a ${PREFIX}/lib/)
-  # set imported library target properties
-  add_dependencies(METIS metis)
-  set_target_properties(METIS PROPERTIES
-    IMPORTED_LOCATION ${PREFIX}/lib/libmetis.a)
-  # set cache variables that would otherwise be set after mfem_find_package call
-  set(METIS_VERSION_5 FALSE CACHE BOOL "Is METIS version 5?")
-  return()
-endif()

 include(MfemCmakeUtilities)
 mfem_find_package(METIS METIS METIS_DIR "include;Lib" "metis.h"
@@ -125,9 +125,7 @@ macro(add_mfem_miniapp MFEM_EXE_NAME)
  if (MFEM_USE_CUDA)
    set_source_files_properties(${MAIN_LIST} ${EXTRA_SOURCES_LIST}
      PROPERTIES LANGUAGE CUDA)
-    if (MFEM_CUDA_COMPILER_IS_NVCC)
-      list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
-    endif()
+    list(TRANSFORM EXTRA_OPTIONS_LIST PREPEND "-Xcompiler=")
  endif()

  # Actually add the executable
@@ -718,7 +716,7 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
  get_target_property(IsImported ${tgt} IMPORTED)
  # message(STATUS "${tgt}[IMPORTED]: ${IsImported}")
  # Generally, the possible target types are: STATIC_LIBRARY, MODULE_LIBRARY,
-  # SHARED_LIBRARY, INTERFACE_LIBRARY, UNKNOWN_LIBRARY, EXECUTABLE.
+  # SHARED_LIBRARY, INTERFACE_LIBRARY, EXECUTABLE.
  get_target_property(type ${tgt} TYPE)
  # message(STATUS "${tgt}[TYPE]: ${type}")
  unset(ImportConfig)
@@ -766,7 +764,7 @@ function(mfem_get_target_options Target CompileOptsVar LinkOptsVar)
    else()
      message(STATUS " *** Warning: [${tgt}] LOCATION not defined!")
    endif()
-  elseif ("${type}" STREQUAL "SHARED_LIBRARY" OR "${type}" STREQUAL "UNKNOWN_LIBRARY")
+  elseif ("${type}" STREQUAL "SHARED_LIBRARY")
    get_target_property(Location ${tgt} LOCATION)
    if (Location)
      get_filename_component(Dir ${Location} DIRECTORY)
@@ -879,8 +877,7 @@ function(mfem_export_mk_files)
      MFEM_USE_OCCA MFEM_USE_CEED MFEM_USE_CALIPER MFEM_USE_UMPIRE MFEM_USE_SIMD
      MFEM_USE_ADIOS2 MFEM_USE_MKL_CPARDISO MFEM_USE_MKL_PARDISO
      MFEM_USE_ADFORWARD MFEM_USE_CODIPACK MFEM_USE_BENCHMARK MFEM_USE_PARELAG
-      MFEM_USE_TRIBOL MFEM_USE_MOONOLITH MFEM_USE_ALGOIM MFEM_USE_ENZYME
-      MFEM_USE_HDF5)
+      MFEM_USE_TRIBOL MFEM_USE_MOONOLITH MFEM_USE_ALGOIM MFEM_USE_ENZYME)
  foreach(var ${CONFIG_MK_BOOL_VARS})
    if (${var})
      set(${var} YES)
@@ -932,14 +929,12 @@ function(mfem_export_mk_files)
  endif()
  set(MFEM_BUILD_TAG "${CMAKE_SYSTEM}")
  set(MFEM_PREFIX "${CMAKE_INSTALL_PREFIX}")
-  # For the next 4 variables, these are the values for the build-tree version of
+  # For the next 4 variable, these are the values for the build-tree version of
  # 'config.mk'
  set(MFEM_INC_DIR "${PROJECT_BINARY_DIR}")
  set(MFEM_LIB_DIR "${PROJECT_BINARY_DIR}")
  set(MFEM_TEST_MK "${PROJECT_SOURCE_DIR}/config/test.mk")
  set(MFEM_CONFIG_EXTRA "MFEM_BUILD_DIR ?= ${PROJECT_BINARY_DIR}")
-  # TODO: CUDA/HIP support:
-  set(MFEM_XLINKER "${CMAKE_CXX_LINKER_WRAPPER_FLAG}")
  set(MFEM_MPIEXEC ${MPIEXEC})
  if (NOT MFEM_MPIEXEC)
    set(MFEM_MPIEXEC "mpirun")
@@ -93,17 +93,17 @@ macro (RESOLVE_LIBRARIES LIBS LINK_LINE)
        set (_directory_list ${_directory_list} ${libpath})
        set (token ${libname})
      endif (token MATCHES "^/")
-      set (_lib "NOTFOUND")
+      set (_lib "NOTFOUND" CACHE FILEPATH "Cleared" FORCE)
      find_library (_lib ${token} HINTS ${_directory_list} ${_root})
      if (_lib)
-        string (REPLACE "//" "/" _lib ${_lib})
+	string (REPLACE "//" "/" _lib ${_lib})
        list (APPEND _libs_found ${_lib})
      else (_lib)
        message (STATUS "Unable to find library ${token}")
      endif (_lib)
-      unset(_lib CACHE)
    endif (token MATCHES "-L([^\" ]+|\"[^\"]+\")")
  endforeach (token)
+  set (_lib "NOTFOUND" CACHE INTERNAL "Scratch variable" FORCE)
  # only the LAST occurrence of each library is required since there should be no circular dependencies
  if (_libs_found)
    list (REVERSE _libs_found)
@@ -23,14 +23,11 @@
 #include "_config.hpp"
 #endif

-#include <cstdint>
-#include <climits>
-
 namespace mfem
 {

 #if (defined(MFEM_USE_CUDA) && defined(__CUDACC__)) || \
-    (defined(MFEM_USE_HIP) && defined(__HIP__))
+    (defined(MFEM_USE_HIP) && defined(__HIPCC__))
 #define MFEM_HOST_DEVICE __host__ __device__
 #else
 #define MFEM_HOST_DEVICE
@@ -132,9 +132,6 @@
 // Enable Conduit support.
 // #define MFEM_USE_CONDUIT

-// Enable functionality based on the HDF5 library
-// #define MFEM_USE_HDF5
-
 // Enable functionality based on the NetCDF library (reading CUBIT files).
 // #define MFEM_USE_NETCDF

@@ -40,7 +40,6 @@ MFEM_USE_GINKGO        = @MFEM_USE_GINKGO@
 MFEM_USE_AMGX          = @MFEM_USE_AMGX@
 MFEM_USE_MAGMA         = @MFEM_USE_MAGMA@
 MFEM_USE_GNUTLS        = @MFEM_USE_GNUTLS@
-MFEM_USE_HDF5          = @MFEM_USE_HDF5@
 MFEM_USE_NETCDF        = @MFEM_USE_NETCDF@
 MFEM_USE_PETSC         = @MFEM_USE_PETSC@
 MFEM_USE_SLEPC         = @MFEM_USE_SLEPC@
@@ -88,7 +87,6 @@ MFEM_BUILD_TAG = @MFEM_BUILD_TAG@
 MFEM_PREFIX    = @MFEM_PREFIX@
 MFEM_INC_DIR   = @MFEM_INC_DIR@
 MFEM_LIB_DIR   = @MFEM_LIB_DIR@
-MFEM_XLINKER   = @MFEM_XLINKER@

 # Location of test.mk
 MFEM_TEST_MK = @MFEM_TEST_MK@
@@ -99,7 +97,7 @@ MFEM_MPIEXEC_NP = @MFEM_MPIEXEC_NP@
 MFEM_MPI_NP     = @MFEM_MPI_NP@

 # The NVCC compiler cannot link with -x=cu
-MFEM_LINK_FLAGS := $(filter-out -x=cu -xcuda -xhip, $(MFEM_FLAGS))
+MFEM_LINK_FLAGS := $(filter-out -x=cu -xhip, $(MFEM_FLAGS))

 # Optional extra configuration
@MFEM_CONFIG_EXTRA@
@@ -43,7 +43,6 @@ option(MFEM_USE_AMGX "Enable AmgX usage" OFF)
 option(MFEM_USE_MAGMA "Enable MAGMA usage" OFF)
 option(MFEM_USE_GNUTLS "Enable GNUTLS usage" OFF)
 option(MFEM_USE_GSLIB "Enable GSLIB usage" OFF)
-option(MFEM_USE_HDF5 "Enable HDF5 usage" OFF)
 option(MFEM_USE_NETCDF "Enable NETCDF usage" OFF)
 option(MFEM_USE_PETSC "Enable PETSc support." OFF)
 option(MFEM_USE_SLEPC "Enable SLEPc support." OFF)
@@ -89,12 +88,6 @@ option(MFEM_ENABLE_EXAMPLES "Build all of the examples" OFF)
 option(MFEM_ENABLE_MINIAPPS "Build all of the miniapps" OFF)
 option(MFEM_ENABLE_BENCHMARKS "Build all of the benchmarks" OFF)

-# Allow a user to specify fetching of certain third-party libraries instead of
-# searching for existing installations.
-option(FETCH_TPLS "Enable fetching of all supported third-party libraries" OFF)
-option(HYPRE_FETCH "Enable fetching of hypre" OFF)
-option(METIS_FETCH "Enable fetching of METIS" OFF)
-
 # Setting CXX/MPICXX on the command line or in user.cmake will overwrite the
 # autodetected C++ compiler.
 # set(CXX g++)
@@ -274,8 +267,6 @@ set(TRIBOL_DIR "${MFEM_DIR}/../tribol" CACHE PATH "Path to Tribol")
 set(Tribol_REQUIRED_PACKAGES "Axom/core/mint/slam/slic" CACHE STRING
    "Additional packages required by Tribol")

-set(ENZYME_DIR "${MFEM_DIR}/../enzyme" CACHE PATH "Path to Enzyme")
-
 set(BLAS_INCLUDE_DIRS "" CACHE STRING "Path to BLAS headers.")
 set(BLAS_LIBRARIES "" CACHE STRING "The BLAS library.")
 set(LAPACK_INCLUDE_DIRS "" CACHE STRING "Path to LAPACK headers.")
@@ -24,7 +24,7 @@ EGREP_BIN = $(shell command -v egrep 2> /dev/null)
 CXX = g++
 MPICXX = mpicxx

-BASE_FLAGS  = -std=c++17
+BASE_FLAGS  = -std=c++11
 OPTIM_FLAGS = -O3 $(BASE_FLAGS)
 DEBUG_FLAGS = -g $(XCOMPILER)-Wall $(BASE_FLAGS)

@@ -43,23 +43,12 @@ SHARED = NO

 # CUDA configuration options
 #
-# If you set MFEM_USE_ENZYME=YES, must use CUDA_CXX=clang++
+# If you set MFEM_USE_ENZYME=YES, CUDA_CXX has to be configured to use cuda with
+# clang as its host compiler.
 CUDA_CXX = nvcc
 CUDA_ARCH = sm_60
-# Base CUDA install directory, only needed if building with clang+cuda:
-# The default setting is:
-# 1. If CUDA_HOME is defined and non-empty, use that.
-# 2. If nvcc is in the path, use the directory two levels up from that.
-# 3. Use /usr/local/cuda
-CUDA_DIR = $(or $(CUDA_HOME),$(patsubst %/,%,$(dir \
- $(patsubst %/,%,$(dir $(shell command -v nvcc))))),/usr/local/cuda)
-# flags for clang+cuda
-CLANG_CUDA_FLAGS = -xcuda --cuda-path=$(CUDA_DIR) --cuda-gpu-arch=$(CUDA_ARCH)
-# flags for nvcc
-NVCC_FLAGS = -x=cu --expt-extended-lambda --expt-relaxed-constexpr \
- -arch=$(CUDA_ARCH) -isystem "$(CUDA_DIR)/include"
-# Prefixes for passing flags to the host compiler and linker when using
-# CUDA_CXX=nvcc
+CUDA_FLAGS = -x=cu --expt-extended-lambda -arch=$(CUDA_ARCH)
+# Prefixes for passing flags to the host compiler and linker when using CUDA_CXX
 CUDA_XCOMPILER = -Xcompiler=
 CUDA_XLINKER   = -Xlinker=

@@ -156,7 +145,6 @@ MFEM_USE_GINKGO        = NO
 MFEM_USE_AMGX          = NO
 MFEM_USE_MAGMA         = NO
 MFEM_USE_GNUTLS        = NO
-MFEM_USE_HDF5          = NO
 MFEM_USE_NETCDF        = NO
 MFEM_USE_PETSC         = NO
 MFEM_USE_SLEPC         = NO
@@ -238,7 +226,7 @@ HYPRE_OPT = -I$(HYPRE_DIR)/include
 HYPRE_LIB = -L$(HYPRE_DIR)/lib -lHYPRE
 ifeq (YES,$(MFEM_USE_CUDA))
   # This is only necessary when hypre is built with cuda:
-   HYPRE_LIB += -lcusolver -lcusparse -lcurand -lcublas
+   HYPRE_LIB += -lcusparse -lcurand -lcublas
 endif
 ifeq (YES,$(MFEM_USE_HIP))
   # This is only necessary when hypre is built with hip:
@@ -253,7 +241,7 @@ ifeq ($(MFEM_USE_SUPERLU)$(MFEM_USE_STRUMPACK)$(MFEM_USE_MUMPS),NONONO)
     METIS_OPT =
     METIS_LIB = -L$(METIS_DIR) -lmetis
   else
-     METIS_DIR = @MFEM_DIR@/../metis-5.1.0
+     METIS_DIR = @MFEM_DIR@/../metis-5.0
     METIS_OPT = -I$(METIS_DIR)/include
     METIS_LIB = -L$(METIS_DIR)/lib -lmetis
   endif
@@ -413,14 +401,9 @@ MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a -lcublas -lcusparse $(LAPACK_LIB)
 GNUTLS_OPT =
 GNUTLS_LIB = -lgnutls

-# HDF5 library configuration
-HDF5_DIR   = $(HOME)/local
-HDF5_OPT = -I$(HDF5_DIR)/include
-HDF5_LIB = $(XLINKER)-rpath,$(HDF5_DIR)/lib -L$(HDF5_DIR)/lib -lhdf5_hl -lhdf5 \
-           $(ZLIB_LIB)
-
 # NetCDF library configuration
 NETCDF_DIR = $(HOME)/local
+HDF5_DIR   = $(HOME)/local
 NETCDF_OPT = -I$(NETCDF_DIR)/include -I$(HDF5_DIR)/include $(ZLIB_OPT)
 NETCDF_LIB = $(XLINKER)-rpath,$(NETCDF_DIR)/lib -L$(NETCDF_DIR)/lib\
 $(XLINKER)-rpath,$(HDF5_DIR)/lib -L$(HDF5_DIR)/lib\
@@ -522,9 +505,6 @@ GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs
 # CUDA library configuration
 CUDA_OPT =
 CUDA_LIB = -lcusparse -lcublas
-CLANG_CUDA_LIB = -L$(CUDA_DIR)/lib64 -L$(CUDA_DIR)/lib \
- $(XLINKER)-rpath,$(CUDA_DIR)/lib64,-rpath,$(CUDA_DIR)/lib \
- -lcudart -ldl -lrt -pthread

 # HIP library configuration
 HIP_OPT =
@@ -624,20 +604,29 @@ TRIBOL_LIB = -L$(TRIBOL_DIR)/lib -ltribol -lredecomp -L$(AXOM_DIR)/lib -laxom_mi
   -laxom_slam -laxom_slic -laxom_core

 # Enzyme configuration
-ENZYME_DIR = @MFEM_DIR@/../enzyme
-ENZYME_PLUGIN = $(abspath $(wildcard $(subst \
-   @MFEM_DIR@,$(MFEM_DIR),$(ENZYME_DIR))/lib/ClangEnzyme-*.$(SO_EXT)))
-ifeq ($(MAKECMDGOALS)-$(MFEM_USE_ENZYME),config-YES)
-   ifeq ($(ENZYME_PLUGIN),)
-      $(error Unable to find the Enzyme pluging! Please set ENZYME_DIR)
-   endif
-   ifneq ($(words $(ENZYME_PLUGIN)),1)
-      $(error Multiple versions of the Enzyme pluging found! \
-              Please set ENZYME_PLUGIN directly)
-   endif
+
+# If you want to enable automatic differentiation at compile time, use the
+# options below, adapted to your configuration. To be more flexible, we
+# recommend using the Enzyme plugin during link time optimization. One option is
+# to add your options to the global compiler/linker flags like
+#
+# BASE_FLAGS += -flto
+# CXX_XLINKER += -fuse-ld=lld -Wl,--lto-legacy-pass-manager\
+#                -Wl,-mllvm=-load=$(ENZYME_DIR)/LLDEnzyme-$(ENZYME_VERSION).so -Wl,
+#
+ENZYME_DIR ?= @MFEM_DIR@/../enzyme
+ENZYME_VERSION ?= 14
+ENZYME_OPT = -fno-experimental-new-pass-manager -Xclang -load -Xclang $(ENZYME_DIR)/ClangEnzyme-$(ENZYME_VERSION).so
+ENZYME_LIB = ""
+
+# Google Benchmark, SUNDIALS >= 6.4.0, STRUMPACK, RAJA, UMPIRE, and Tribol require C++14:
+ifneq ($(filter YES,$(MFEM_USE_BENCHMARK) $(MFEM_USE_SUNDIALS) $(MFEM_USE_STRUMPACK) $(MFEM_USE_RAJA) $(MFEM_USE_UMPIRE) $(MFEM_USE_TRIBOL)),)
+    BASE_FLAGS = -std=c++14
+endif
+# Ginkgo requires C++17:
+ifeq ($(MFEM_USE_GINKGO),YES)
+   BASE_FLAGS = -std=c++17
 endif
-ENZYME_OPT = -fplugin=$(ENZYME_PLUGIN)
-ENZYME_LIB =

 # If YES, enable some informational messages
 VERBOSE = NO
@@ -115,7 +115,7 @@ vertices

 nodes
 FiniteElementSpace
-FiniteElementCollection: H1_3D_P2
+FiniteElementCollection: Quadratic
 VDim: 3
 Ordering: 0

@@ -56,7 +56,7 @@ vertices

 nodes
 FiniteElementSpace
-FiniteElementCollection: H1_3D_P2
+FiniteElementCollection: Quadratic
 VDim: 3
 Ordering: 0

@@ -1,593 +0,0 @@
-MFEM mesh v1.0
-
-# Created by: Pointwise
-
-# MFEM Geometry Types:
-#
-# POINT       = 0
-# SEGMENT     = 1
-# TRIANGLE    = 2
-# SQUARE      = 3
-# TETRAHEDRON = 4
-# CUBE        = 5
-# PRISM       = 6
-
-dimension
-2
-
-elements
-160
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-1 3 164 165 162 163
-1 3 2 166 164 1
-1 3 166 132 165 164
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-1 3 5 169 168 4
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-1 3 6 170 169 5
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-1 3 6 7 176 171
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-
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-MFEM NURBS NC-patch mesh v1.0
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@@ -227,7 +227,7 @@ vertices

 nodes
 FiniteElementSpace
-FiniteElementCollection: H1_2D_P2
+FiniteElementCollection: Quadratic
 VDim: 2
 Ordering: 0

@@ -65,7 +65,7 @@ vertices

 nodes
 FiniteElementSpace
-FiniteElementCollection: H1_2D_P2
+FiniteElementCollection: Quadratic
 VDim: 2
 Ordering: 0

@@ -48,7 +48,7 @@ PROJECT_NAME           = MFEM
 # could be handy for archiving the generated documentation or if some version
 # control system is used.

-PROJECT_NUMBER         = v4.8.1
+PROJECT_NUMBER         = v4.8.0

 # Using the PROJECT_BRIEF tag one can provide an optional one line description
 # for a project that appears at the top of each page and should give viewer a
@@ -951,7 +951,6 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/fem/ceed/integrators/nlconvection \
                         @MFEM_SOURCE_DIR@/fem/ceed/interface \
                         @MFEM_SOURCE_DIR@/fem/ceed/solvers \
-                         @MFEM_SOURCE_DIR@/fem/dfem \
                         @MFEM_SOURCE_DIR@/fem/eltrans \
                         @MFEM_SOURCE_DIR@/fem/fe \
                         @MFEM_SOURCE_DIR@/fem/gslib \
@@ -960,6 +959,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/fem/moonolith \
                         @MFEM_SOURCE_DIR@/fem/qinterp \
                         @MFEM_SOURCE_DIR@/fem/tmop \
+                         @MFEM_SOURCE_DIR@/fem/darcy \
                         @MFEM_SOURCE_DIR@/examples \
                         @MFEM_SOURCE_DIR@/examples/amgx \
                         @MFEM_SOURCE_DIR@/examples/caliper \
@@ -973,7 +973,6 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/miniapps/adjoint \
                         @MFEM_SOURCE_DIR@/miniapps/autodiff \
                         @MFEM_SOURCE_DIR@/miniapps/common \
-                         @MFEM_SOURCE_DIR@/miniapps/dfem \
                         @MFEM_SOURCE_DIR@/miniapps/dpg \
                         @MFEM_SOURCE_DIR@/miniapps/dpg/util \
                         @MFEM_SOURCE_DIR@/miniapps/electromagnetics \
@@ -202,7 +202,6 @@ namespace mfem {
 * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code
 * - <a class="el" href="maxwell_8cpp_source.html">Maxwell</a>: simple transient full-wave electromagnetics simulation code
 * - <a class="el" href="joule_8cpp_source.html">Joule</a>: transient magnetics and Joule heating miniapp
- * - <a class="el" href="lorentz_8cpp_source.html">Lorentz</a>: simple particle tracking code based on the Lorentz force
 * - <a class="el" href="classmfem_1_1navier_1_1NavierSolver.html">Navier</a>: solve the transient incompressible Navier-Stokes equations
 * - <a class="el" href="mobius-strip_8cpp_source.html">Mobius Strip</a>: generate various Mobius strip-like meshes
 * - <a class="el" href="klein-bottle_8cpp_source.html">Klein Bottle</a>: generate three types of Klein bottle surfaces
@@ -205,15 +205,6 @@ if (MFEM_ENABLE_TESTING)
      $<TARGET_FILE:ex25p> "-no-vis" "--mumps-solver"
      ${MPIEXEC_POSTFLAGS})
  endif()
-
-  # Parallel libCEED example
-  if (MFEM_USE_CEED AND MFEM_USE_MPI)
-    add_test(NAME ex1p_ceed_np=${MFEM_MPI_NP}
-      COMMAND ${MPIEXEC} ${MPIEXEC_NUMPROC_FLAG} ${MFEM_MPI_NP}
-      ${MPIEXEC_PREFLAGS}
-      $<TARGET_FILE:ex1p> "-no-vis" "-d ceed-cpu" "-pa" "-a"
-      ${MPIEXEC_POSTFLAGS})
-  endif()
 endif()

 # Include the examples/amgx directory if AmgX is enabled
@@ -0,0 +1,794 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#include "coupledop.hpp"
+
+namespace mfem
+{
+CoupledOperator::CoupledOperator(const Array<int> &bdr_u_is_ess,
+                                 const Array<int> &bdr_E_is_ess, Coefficient *sigma_,
+                                 const Array<LinearForm*> &lfs_, const Array<Coefficient*> &coeffs_,
+                                 FiniteElementSpace *u_space_, FiniteElementSpace *n_space_,
+                                 FiniteElementSpace *E_space_, FiniteElementSpace *B_space_,
+                                 FiniteElementSpace *tr_space_, real_t td)
+   : TimeDependentOperator(0, IMPLICIT), sigma(sigma_), lfs(lfs_),
+     coeffs(coeffs_), u_space(u_space_), n_space(n_space_),
+     E_space(E_space_), B_space(B_space_), tr_space(tr_space_)
+{
+   offsets = ConstructOffsets(u_space, n_space, E_space, B_space, tr_space);
+
+   width = height = offsets.Last();
+
+   //plasma
+
+   const int dim = u_space->GetMesh()->Dimension();
+   const bool fec_disc = (u_space->FEColl()->GetContType() ==
+                          FiniteElementCollection::DISCONTINUOUS);
+   const bool fec_vec = (u_space->FEColl()->GetRangeType(dim) ==
+                         FiniteElement::VECTOR);
+   const bool dg = (fec_disc && !fec_vec);
+   const bool brt = (fec_disc && fec_vec);
+
+   if (!dg)
+   {
+      u_space->GetEssentialTrueDofs(bdr_u_is_ess, ess_u_tdofs_list);
+   }
+
+   darcy = new DarcyForm(u_space, n_space);
+
+   Mu = darcy->GetFluxMassForm();
+   Mn = darcy->GetPotentialMassForm();
+   Du = darcy->GetFluxDivForm();
+
+   idtcoeff = new FunctionCoefficient([&](const Vector &) { return idt; });
+   dtcoeff = new FunctionCoefficient([&](const Vector &) { return 1./idt; });
+
+   if (dg)
+   {
+      Mu->AddDomainIntegrator(new VectorMassIntegrator(*idtcoeff));
+   }
+   else
+   {
+      Mu->AddDomainIntegrator(new VectorFEMassIntegrator(idtcoeff));
+   }
+
+   if (dg)
+   {
+      Du->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      Du->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                       new DGNormalTraceIntegrator(-1.)));
+      Du->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
+                                                          -1.)), const_cast<Array<int>&>(bdr_u_is_ess));
+   }
+   else
+   {
+      Du->AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+      if (brt)
+      {
+         Du->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+         Du->AddBdrFaceIntegrator(new TransposeIntegrator(new DGNormalTraceIntegrator(
+                                                             -1.)), const_cast<Array<int>&>(bdr_u_is_ess));
+      }
+   }
+
+   if (dg && td > 0.)
+   {
+      Mn->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(*dtcoeff, td));
+      Mn->AddBdrFaceIntegrator(new HDGDiffusionIntegrator(*dtcoeff, td),
+                               const_cast<Array<int>&>(bdr_u_is_ess));
+   }
+
+   Mn->AddDomainIntegrator(new MassIntegrator(*idtcoeff));
+
+   if (tr_space)
+   {
+      darcy->EnableHybridization(tr_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_u_tdofs_list);
+   }
+
+   //Maxwell
+
+   E_space->GetEssentialTrueDofs(bdr_E_is_ess, ess_E_tdofs_list);
+
+   ME = new BilinearForm(E_space);
+   ME->AddDomainIntegrator(new VectorFEMassIntegrator());
+   CE = new MixedBilinearForm(E_space, B_space);
+   CE->AddDomainIntegrator(new MixedCurlIntegrator());
+   CdE = new DiscreteLinearOperator(E_space, B_space);
+   CdE->AddDomainInterpolator(new CurlInterpolator());
+
+   ME->Assemble();
+   ME->Finalize();
+
+   CE->Assemble();
+   CE->Finalize();
+
+   CdE->Assemble();
+   CdE->Finalize();
+}
+
+CoupledOperator::~CoupledOperator()
+{
+   delete ME;
+   delete CE;
+   delete CdE;
+   delete darcy;
+   delete idtcoeff;
+   delete dtcoeff;
+}
+
+Array<int> CoupledOperator::ConstructOffsets(const FiniteElementSpace *u_space,
+                                             const FiniteElementSpace *n_space, const FiniteElementSpace *E_space,
+                                             const FiniteElementSpace *B_space, const FiniteElementSpace *trace_space)
+{
+   Array<int> offsets((trace_space)?(6):(5));
+   int i = 0;
+   offsets[i++] = 0;
+   offsets[i++] = u_space->GetVSize();
+   offsets[i++] = n_space->GetVSize();
+   if (trace_space)
+   {
+      offsets[i++] = trace_space->GetVSize();
+   }
+   offsets[i++] = E_space->GetVSize();
+   offsets[i++] = B_space->GetVSize();
+   offsets.PartialSum();
+
+   return offsets;
+}
+
+void CoupledOperator::ImplicitSolve(const double dt, const Vector &x, Vector &y)
+{
+   const bool time_track = false;
+
+   BlockVector bx(const_cast<Vector&>(x), offsets);
+   BlockVector by(y, offsets);
+
+   int i = 0;
+   const Vector &un = bx.GetBlock(i++);
+   const Vector &nn = bx.GetBlock(i++);
+   if (tr_space) { i++; }
+   const Vector &En = bx.GetBlock(i++);
+   const Vector &Bn = bx.GetBlock(i++);
+
+   i = 2;
+   //Vector &u = by.GetBlock(i++);
+   //Vector &n = by.GetBlock(i++);
+   if (tr_space) { i++; }
+   Vector &E = by.GetBlock(i++);
+   Vector &B = by.GetBlock(i++);
+
+   //offsets
+
+   Array<int> X_offsets(3);
+   X_offsets[0] = 0;
+   if (tr_space)
+   {
+      X_offsets[1] = tr_space->GetVSize();
+   }
+   else
+   {
+      X_offsets[1] = darcy->Width();
+   }
+   X_offsets[2] = E_space->GetVSize();
+   X_offsets.PartialSum();
+
+   //solution & rhs vectors
+
+   BlockVector X(X_offsets), RHS(X_offsets);
+   BlockDiagonalPreconditioner bprec(X_offsets);
+   bprec.owns_blocks = true;
+
+   //plasma
+
+   LinearForm *g = lfs[0];
+   LinearForm *f = lfs[1];
+   LinearForm *h = lfs[2];
+
+   //set time
+
+   for (Coefficient *coeff : coeffs)
+   {
+      coeff->SetTime(t);
+   }
+
+   //assemble rhs
+
+   StopWatch chrono;
+   if (time_track)
+   {
+      chrono.Clear();
+      chrono.Start();
+   }
+
+   g->Assemble();
+   f->Assemble();
+   if (h) { h->Assemble(); }
+
+   //check if the operator has to be reassembled
+
+   bool reassemble = (idt != 1./dt);
+
+   if (reassemble)
+   {
+      idt = 1./dt;
+
+      //reset the operator
+
+      darcy->Update();
+
+      //assemble the system
+      darcy->Assemble();
+
+      if (Mu && tr_space)
+      {
+         Mu->Update();
+         Mu->Assemble();
+         //Mq0->Finalize();
+      }
+      if (Mn && tr_space)
+      {
+         Mn->Update();
+         Mn->Assemble();
+         //Mt0->Finalize();
+      }
+   }
+
+   if (Mu)
+   {
+      GridFunction u_h;
+      u_h.MakeRef(darcy->FluxFESpace(), const_cast<Vector&>(un), 0);
+      Mu->AddMult(u_h, *g, +1.);
+   }
+
+   if (Mn)
+   {
+      GridFunction p_h;
+      p_h.MakeRef(darcy->PotentialFESpace(), const_cast<Vector&>(nn), 0);
+      Mn->AddMult(p_h, *f, -1.);
+   }
+
+   //form the reduced system
+
+   OperatorHandle op_pl;
+   BlockVector darcy_x(const_cast<Vector&>(x), darcy->GetOffsets());
+   BlockVector darcy_rhs(g->GetData(), darcy->GetOffsets());
+   BlockVector X_pl;
+   BlockVector RHS_pl;
+   Array<int> tr_offsets(2);
+
+   if (tr_space)
+   {
+      tr_offsets[0] = 0;
+      tr_offsets[1] = tr_space->GetVSize();
+      X_pl.Update(X, tr_offsets);
+      RHS_pl.Update(RHS, tr_offsets);
+      if (h)
+      {
+         RHS_pl.Vector::operator=(*h);
+      }
+      else
+      {
+         RHS_pl = 0.;
+      }
+      darcy->FormLinearSystem(ess_u_tdofs_list, darcy_x, darcy_rhs,
+                              op_pl, X_pl, RHS_pl);
+   }
+   else
+   {
+      X_pl.Update(X, darcy->GetOffsets());
+      RHS_pl.Update(RHS, darcy->GetOffsets());
+      X_pl = darcy_x;
+      RHS_pl = darcy_rhs;
+      BlockVector darcy_x_tmp(X_pl, darcy->GetOffsets());
+      BlockVector darcy_rhs_tmp(RHS_pl, darcy->GetOffsets());
+      darcy->FormLinearSystem(ess_u_tdofs_list, darcy_x_tmp, darcy_rhs_tmp,
+                              op_pl, X_pl, RHS_pl);
+   }
+
+   if (time_track)
+   {
+      chrono.Stop();
+      std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+   }
+
+   if (tr_space)
+   {
+      bprec.SetDiagonalBlock(0, new DSmoother(*op_pl.As<SparseMatrix>()));
+   }
+   else
+   {
+      BlockDiagonalPreconditioner *darcy_prec = new BlockDiagonalPreconditioner(
+         darcy->GetOffsets());
+      darcy_prec->owns_blocks = true;;
+      darcy_prec->SetDiagonalBlock(0, new GSSmoother(Mu->SpMat()));
+      darcy_prec->SetDiagonalBlock(1, new DSmoother(Mn->SpMat()));
+      bprec.SetDiagonalBlock(0, darcy_prec);
+   }
+
+   //Maxwell
+
+   TransposeOperator Ct(CE);
+   ProductOperator CtCd(&Ct, CdE, false, false);
+   SumOperator MECtCd(ME, 1., &CtCd, dt*dt, false, false);
+
+   Vector &X_max = X.GetBlock(1);
+   X_max = En;
+
+   Vector &RHS_max = RHS.GetBlock(1);
+   ME->Mult(En, RHS_max);
+   //MECtCd.Mult(En, rhs);
+   CE->AddMultTranspose(Bn, RHS_max, dt);
+   //CtCd.AddMult(En, rhs, +dt*dt/2.);
+
+   //ME - dt*c2/2*Ct(Bn-dt*CE) = MEn + dt*c2/2CtBn
+   //(M + dt2*c2/2*Ct*C)E = MEn + dt*c2*CtBn
+   //ME - dt*c2*Ct(Bn-dt/2*CE-dt/2*CEn) = MEn
+   //(M + dt2*c2/2*Ct*C)E = MEn + dt*c2CtBn - dt2*c2/2*CtCEn
+   //-1/dt B - CE = 0
+
+   //ME->EliminateVDofsInRHS(ess_tdof_list, En, rhs);
+
+   ConstrainedOperator op_max(&MECtCd, ess_E_tdofs_list);
+
+   //op_max.EliminateRHS(En, RHS_max);
+
+   bprec.SetDiagonalBlock(1, new DSmoother(ME->SpMat()));
+
+   //coupling
+
+   /*const Mesh *mesh = n_space->GetMesh();
+   const int NE = mesh->GetNE();
+   for (int el = 0; el < NE; el++)
+   {
+
+   }*/
+
+   ReducedOperator bop(sigma, darcy, E_space, *op_pl.Ptr(), op_max);
+   if (tr_space)
+   {
+      Array<int> ess_tr_tdofs_list;//dummy
+      bop.SetEssentialTDOFs(ess_tr_tdofs_list, ess_E_tdofs_list);
+      bop.SetDarcyRHS(darcy_rhs);
+   }
+   else
+   {
+      bop.SetEssentialTDOFs(ess_u_tdofs_list, ess_E_tdofs_list);
+   }
+   bop.EliminateRHS(X, RHS);
+
+   //solve
+
+   GMRESSolver solver;
+   solver.SetMaxIter(1000);
+   solver.SetAbsTol(0.);
+   solver.SetRelTol(1e-6);
+   solver.SetOperator(bop);
+   solver.SetPreconditioner(bprec);
+   solver.SetPrintLevel(0);
+
+   NewtonSolver newton;
+   newton.SetMaxIter(1000);
+   newton.SetAbsTol(0.);
+   newton.SetRelTol(1e-5);
+   newton.SetOperator(bop);
+   newton.SetSolver(solver);
+   newton.SetPrintLevel(1);
+
+   if (time_track)
+   {
+      chrono.Clear();
+      chrono.Start();
+   }
+
+   newton.Mult(RHS, X);
+
+   if (time_track)
+   {
+      chrono.Stop();
+   }
+
+   if (newton.GetConverged())
+   {
+      std::cout << " converged in " << newton.GetNumIterations()
+                << " iterations with a residual norm of " << newton.GetFinalNorm()
+                << ".\n";
+   }
+   else
+   {
+      std::cout << " did not converge in " << newton.GetNumIterations()
+                << " iterations. Residual norm is " << newton.GetFinalNorm()
+                << ".\n";
+   }
+   if (time_track) { std::cout << "Solver took " << chrono.RealTime() << "s.\n"; }
+
+   //recover solution
+
+   BlockVector darcy_y(y, darcy->GetOffsets());
+   darcy_y = darcy_x;
+
+   if (tr_space)
+   {
+      darcy->RecoverFEMSolution(X_pl, darcy_rhs, darcy_y);
+      Vector &darcy_tr = by.GetBlock(2);
+      darcy_tr = X_pl;
+      darcy_tr -= bx.GetBlock(2);
+      darcy_tr *= idt;
+   }
+   else
+   {
+      darcy->RecoverFEMSolution(X_pl, RHS_pl, X_pl);
+      darcy_y = X_pl;
+   }
+
+   darcy_y -= darcy_x;
+   darcy_y *= idt;
+
+   E = X_max;
+
+   E -= En;
+   E *= idt;
+
+   CdE->Mult(En, B);
+   //CdE->AddMult(E, B);
+   //B *= -1./2.;
+   B.Neg();
+}
+CoupledOperator::ReducedOperator::ReducedOperator(Coefficient *sigma_,
+                                                  DarcyForm *darcy_, FiniteElementSpace *fes_E_, Operator &pl, Operator &max)
+   : sigma(sigma_), darcy(darcy_), fes_E(fes_E_)
+{
+   offsets.SetSize(3);
+   offsets[0] = 0;
+   offsets[1] = pl.Width();
+   offsets[2] = max.Width();
+   offsets.PartialSum();
+
+   width = height = offsets.Last();
+
+   if (darcy->GetHybridization())
+   {
+      offsets_x = offsets;
+   }
+   else
+   {
+      offsets_x.SetSize(4);
+      offsets_x[0] = 0;
+      offsets_x[1] = darcy->FluxFESpace()->GetVSize();
+      offsets_x[2] = darcy->PotentialFESpace()->GetVSize();
+      offsets_x[3] = fes_E->GetVSize();
+      offsets_x.PartialSum();
+   }
+
+   BlockOperator *bop = new BlockOperator(offsets);
+   bop->SetDiagonalBlock(0, &pl);
+   bop->SetDiagonalBlock(1, &max);
+
+   op.Reset(bop);
+}
+
+CoupledOperator::ReducedOperator::~ReducedOperator()
+{
+}
+
+void CoupledOperator::ReducedOperator::SetEssentialTDOFs(
+   const Array<int> &u_tdofs_list, const Array<int> &E_tdofs_list)
+{
+   ess_tdofs_list.DeleteAll();
+   ess_tdofs_list.Append(u_tdofs_list);
+   ess_tdofs_list.Append(E_tdofs_list);
+   const int size = ess_tdofs_list.Size();
+   for (int i = 0; i < E_tdofs_list.Size(); i++)
+   {
+      int &tdof = ess_tdofs_list[size - 1 - i];
+      if (tdof >= 0)
+      {
+         tdof += offsets[1];
+      }
+      else
+      {
+         tdof -= offsets[1];
+      }
+   }
+}
+
+void CoupledOperator::ReducedOperator::EliminateRHS(const Vector &x,
+                                                    Vector &b) const
+{
+   if (ess_tdofs_list.Size() <= 0) { return; }
+
+   Vector w(x.Size()), z(b.Size());
+
+   w = 0.;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      w(tdof) = x(tdof);
+   }
+
+   MultUnconstrained(w, z);
+   b -= z;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      b(tdof) = x(tdof);
+   }
+}
+
+void CoupledOperator::ReducedOperator::Mult(const Vector &x, Vector &y) const
+{
+   Vector z(x.Size());
+   z = x;
+
+   for (int tdof : ess_tdofs_list)
+   {
+      z(tdof) = 0.;
+   }
+
+   MultUnconstrained(z, y);
+
+   for (int tdof : ess_tdofs_list)
+   {
+      y(tdof) = x(tdof);
+   }
+}
+
+void CoupledOperator::ReducedOperator::MultUnconstrained(const Vector &x,
+                                                         Vector &y) const
+{
+   op->Mult(x, y);
+
+   const bool hybr = darcy->GetHybridization() != NULL;
+
+   BlockVector bx(const_cast<Vector&>(x), offsets_x);
+   BlockVector by(const_cast<Vector&>(y), offsets_x);
+   BlockVector darcy_x;
+
+   if (hybr)
+   {
+      darcy_x.Update(darcy->GetOffsets());
+      darcy->GetHybridization()->ComputeSolution(*darcy_rhs, x, darcy_x);
+      darcy_rhs->Vector::operator=(darcy_rhs_lin);
+   }
+
+   const Vector &xn = ((hybr)?(darcy_x):(bx)).GetBlock(1);
+   const Vector &xE = bx.GetBlock((hybr)?(1):(2));
+   Vector &yu = ((hybr)?(*darcy_rhs):(by)).GetBlock(0);
+   Vector &yE = by.GetBlock((hybr)?(1):(2));
+
+   Mesh *mesh = fes_E->GetMesh();
+   FiniteElementSpace *fes_u = darcy->FluxFESpace();
+   FiniteElementSpace *fes_n = darcy->PotentialFESpace();
+   Array<int> vdofs_u, dofs_n, vdofs_E;
+   DenseMatrix vshape_u, vshape_E;
+   Vector shape_u, shape_E, shape_n, n_z, E_z, E, bu_z, bE_z;
+
+   for (int z = 0; z < mesh->GetNE(); z++)
+   {
+      ElementTransformation *Tr = mesh->GetElementTransformation(z);
+      const FiniteElement *fe_u = fes_u->GetFE(z);
+      const FiniteElement *fe_n = fes_n->GetFE(z);
+      const FiniteElement *fe_E = fes_E->GetFE(z);
+      const int sdim = Tr->GetSpaceDim();
+      const int ndof_u = fe_u->GetDof();
+      const int ndof_n = fe_n->GetDof();
+
+      fes_u->GetElementVDofs(z, vdofs_u);
+      fes_n->GetElementDofs(z, dofs_n);
+      fes_E->GetElementVDofs(z, vdofs_E);
+
+      if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+      {
+         vshape_u.SetSize(vdofs_u.Size(), sdim);
+      }
+      shape_u.SetSize(ndof_u);
+      shape_n.SetSize(ndof_n);
+      vshape_E.SetSize(vdofs_E.Size(), sdim);
+      shape_E.SetSize(vdofs_E.Size());
+      E.SetSize(sdim);
+
+      bu_z.SetSize(vdofs_u.Size());
+      bE_z.SetSize(vdofs_E.Size());
+      bu_z = 0.;
+      bE_z = 0.;
+
+      xn.GetSubVector(dofs_n, n_z);
+      xE.GetSubVector(vdofs_E, E_z);
+
+      const int order = std::max(fe_E->GetOrder(), fe_n->GetOrder()) * 2 + 1;
+      const IntegrationRule &ir = IntRules.Get(fe_n->GetGeomType(), order);
+      for (int q = 0; q < ir.GetNPoints(); q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         Tr->SetIntPoint(&ip);
+         fe_n->CalcShape(ip, shape_n);
+         const real_t n = n_z * shape_n;
+
+         fe_E->CalcVShape(*Tr, vshape_E);
+         vshape_E.MultTranspose(E_z, E);
+
+         real_t w = n * Tr->Weight();
+         if (sigma) { w *= sigma->Eval(*Tr, ip); }
+
+         if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+         {
+            fe_u->CalcVShape(*Tr, vshape_u);
+            vshape_u.Mult(E, shape_u);
+            bu_z.Add(w, shape_u);
+         }
+         else
+         {
+            fe_u->CalcShape(ip, shape_u);
+            for (int d = 0; d < sdim; d++)
+               for (int i = 0; i < ndof_u; i++)
+               {
+                  bu_z(i+d*ndof_u) += w * E(d) * shape_u(i);
+               }
+         }
+         vshape_E.Mult(E, shape_E);
+         bE_z.Add(w, shape_E);
+      }
+
+      if (hybr) { bu_z.Neg(); }
+
+      yu.AddElementVector(vdofs_u, bu_z);
+      yE.AddElementVector(vdofs_E, bE_z);
+   }
+
+   if (hybr)
+   {
+      BlockVector darcy_Xrhs(darcy->GetOffsets());
+      add(darcy_rhs_lin, -1., *darcy_rhs, darcy_Xrhs);
+      darcy->GetHybridization()->ReduceRHS(darcy_Xrhs, by.GetBlock(0));
+   }
+}
+
+Operator &CoupledOperator::ReducedOperator::GetGradient(const Vector &x) const
+{
+   if (darcy->GetHybridization())
+   {
+      //TODO: coupling terms
+      return const_cast<Operator&>(*op);
+   }
+
+   grad.Clear();
+
+   FiniteElementSpace *fes_u = darcy->FluxFESpace();
+   FiniteElementSpace *fes_n = darcy->PotentialFESpace();
+
+   SparseMatrix *BEE, *BEu, *BnE, *Bnu;
+
+   BEE = new SparseMatrix(fes_E->GetVSize());
+   BEu = new SparseMatrix(fes_u->GetVSize(), fes_E->GetVSize());
+   BnE = new SparseMatrix(fes_E->GetVSize(), fes_n->GetVSize());
+   Bnu = new SparseMatrix(fes_u->GetVSize(), fes_n->GetVSize());
+
+   BlockVector bx(const_cast<Vector&>(x), offsets_x);
+
+   Mesh *mesh = fes_E->GetMesh();
+
+   Array<int> vdofs_u, dofs_n, vdofs_E;
+   DenseMatrix vshape_u, vshape_E;
+   DenseMatrix BEE_z, BEu_z, BnE_z, Bnu_z;
+   Vector shape_u, shape_E, shape_n, n_z, E_z, E;
+
+   for (int z = 0; z < mesh->GetNE(); z++)
+   {
+      ElementTransformation *Tr = mesh->GetElementTransformation(z);
+      const FiniteElement *fe_u = fes_u->GetFE(z);
+      const FiniteElement *fe_n = fes_n->GetFE(z);
+      const FiniteElement *fe_E = fes_E->GetFE(z);
+      const int sdim = Tr->GetSpaceDim();
+      const int ndof_u = fe_u->GetDof();
+      const int ndof_n = fe_n->GetDof();
+
+      fes_u->GetElementVDofs(z, vdofs_u);
+      fes_n->GetElementDofs(z, dofs_n);
+      fes_E->GetElementVDofs(z, vdofs_E);
+
+      if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+      {
+         vshape_u.SetSize(vdofs_u.Size(), sdim);
+      }
+      shape_u.SetSize(ndof_u);
+      shape_n.SetSize(ndof_n);
+      vshape_E.SetSize(vdofs_E.Size(), sdim);
+      shape_E.SetSize(vdofs_E.Size());
+      E.SetSize(sdim);
+
+      BEE_z.SetSize(vdofs_E.Size());
+      BEu_z.SetSize(vdofs_u.Size(), vdofs_E.Size());
+      BnE_z.SetSize(vdofs_E.Size(), dofs_n.Size());
+      Bnu_z.SetSize(vdofs_u.Size(), dofs_n.Size());
+      BEE_z = 0.;
+      BEu_z = 0.;
+      BnE_z = 0.;
+      Bnu_z = 0.;
+
+      bx.GetBlock(1).GetSubVector(dofs_n, n_z);
+      bx.GetBlock(2).GetSubVector(vdofs_E, E_z);
+
+      const int order = std::max(fe_E->GetOrder(), fe_n->GetOrder()) * 2 + 1;
+      const IntegrationRule &ir = IntRules.Get(fe_n->GetGeomType(), order);
+      for (int q = 0; q < ir.GetNPoints(); q++)
+      {
+         const IntegrationPoint &ip = ir.IntPoint(q);
+         Tr->SetIntPoint(&ip);
+         fe_n->CalcShape(ip, shape_n);
+         const real_t n = n_z * shape_n;
+
+         fe_E->CalcVShape(*Tr, vshape_E);
+         vshape_E.MultTranspose(E_z, E);
+
+         real_t w = Tr->Weight();
+         if (sigma) { w *= sigma->Eval(*Tr, ip); }
+
+         if (fe_u->GetRangeType() == FiniteElement::VECTOR)
+         {
+            fe_u->CalcVShape(*Tr, vshape_u);
+            vshape_u.Mult(E, shape_u);
+            AddMult_a_VWt(w, shape_u, shape_n, Bnu_z);
+            AddMult_a_ABt(w * n, vshape_u, vshape_E, BEu_z);
+         }
+         else
+         {
+            fe_u->CalcShape(ip, shape_u);
+            for (int d = 0; d < sdim; d++)
+               for (int i = 0; i < ndof_u; i++)
+               {
+                  for (int j = 0; j < ndof_n; j++)
+                  {
+                     Bnu_z(i+d*ndof_u, j) += w * E(d) * shape_u(i) * shape_n(j);
+                  }
+
+                  for (int j = 0; j < vdofs_E.Size(); j++)
+                  {
+                     BEu_z(i+d*ndof_u, j) += w * n * shape_u(i) * vshape_E(j, d);
+                  }
+               }
+         }
+         vshape_E.Mult(E, shape_E);
+
+         AddMult_a_AAt(w * n, vshape_E, BEE_z);
+         AddMult_a_VWt(w, shape_E, shape_n, BnE_z);
+      }
+
+      BEE->AddSubMatrix(vdofs_E, vdofs_E, BEE_z);
+      BEu->AddSubMatrix(vdofs_u, vdofs_E, BEu_z);
+      BnE->AddSubMatrix(vdofs_E, dofs_n, BnE_z);
+      Bnu->AddSubMatrix(vdofs_u, dofs_n, Bnu_z);
+   }
+
+   BEE->Finalize();
+   BEu->Finalize();
+   BnE->Finalize();
+   Bnu->Finalize();
+
+   BlockOperator *bcouple = new BlockOperator(offsets_x);
+   bcouple->owns_blocks = true;
+   bcouple->SetBlock(2, 2, BEE);
+   bcouple->SetBlock(0, 2, BEu);
+   bcouple->SetBlock(2, 1, BnE);
+   bcouple->SetBlock(0, 1, Bnu);
+
+   grad.Reset(new SumOperator(op.Ptr(), 1., bcouple, 1., false, true));
+
+   if (ess_tdofs_list.Size() > 0)
+   {
+      grad.SetOperatorOwner(false);
+      grad.Reset(new ConstrainedOperator(grad.Ptr(), ess_tdofs_list));
+   }
+
+   return *grad;
+}
+}
@@ -0,0 +1,79 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_COUPLEDOP
+#define MFEM_COUPLEDOP
+
+#include "mfem.hpp"
+
+namespace mfem
+{
+class CoupledOperator : public TimeDependentOperator
+{
+   Array<int> ess_u_tdofs_list, ess_E_tdofs_list;
+   Coefficient *sigma;
+   const Array<LinearForm*> &lfs;
+   const Array<Coefficient*> &coeffs;
+   FiniteElementSpace *u_space, *n_space, *E_space, *B_space, *tr_space;
+   Array<int> offsets;
+   BilinearForm *ME{}, *Mu{}, *Mn{};
+   MixedBilinearForm *CE{}, *Du{};
+   DiscreteLinearOperator *CdE{};
+   DarcyForm *darcy{};
+   real_t idt{};
+   Coefficient *idtcoeff{}, *dtcoeff{};
+
+   class ReducedOperator : public Operator
+   {
+      Array<int> offsets, offsets_x;
+      Coefficient *sigma;
+      DarcyForm *darcy;
+      BlockVector *darcy_rhs{};
+      Vector darcy_rhs_lin;
+      FiniteElementSpace *fes_E;
+      OperatorHandle op;
+      Array<int> ess_tdofs_list;
+      mutable OperatorHandle grad;
+
+   public:
+      ReducedOperator(Coefficient *sigma, DarcyForm *darcy, FiniteElementSpace *fes_E,
+                      Operator &pl, Operator &max);
+      ~ReducedOperator();
+
+      void SetEssentialTDOFs(const Array<int> &u_tdofs_list,
+                             const Array<int> &E_tdofs_list);
+      void SetDarcyRHS(BlockVector &rhs) { darcy_rhs = &rhs; darcy_rhs_lin = rhs; }
+      void EliminateRHS(const Vector &x, Vector &b) const;
+
+      void Mult(const Vector &x, Vector &y) const override;
+      void MultUnconstrained(const Vector &x, Vector &y) const;
+      Operator& GetGradient(const Vector &x) const override;
+   };
+
+public:
+   CoupledOperator(const Array<int> &bdr_u_ess, const Array<int> &bdr_E_is_ess,
+                   Coefficient *sigma,
+                   const Array<LinearForm*> &lfs, const Array<Coefficient*> &coeffs,
+                   FiniteElementSpace *u_space, FiniteElementSpace *n_space,
+                   FiniteElementSpace *E_space, FiniteElementSpace *B_space,
+                   FiniteElementSpace *tr_space = NULL, real_t td = 0.5);
+   ~CoupledOperator();
+
+   static Array<int> ConstructOffsets(
+      const FiniteElementSpace *u_space, const FiniteElementSpace *n_space,
+      const FiniteElementSpace *E_space, const FiniteElementSpace *B_space,
+      const FiniteElementSpace *tr_space = NULL);
+
+   void ImplicitSolve(const double dt, const Vector &x, Vector &y) override;
+};
+}
+
+#endif
@@ -0,0 +1,226 @@
+// Copyright (c) 2010-2024, Lawrence Livermore National Security, LLC. Produced
+// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
+// LICENSE and NOTICE for details. LLNL-CODE-806117.
+//
+// This file is part of the MFEM library. For more information and source code
+// availability visit https://mfem.org.
+//
+// MFEM is free software; you can redistribute it and/or modify it under the
+// terms of the BSD-3 license. We welcome feedback and contributions, see file
+// CONTRIBUTING.md for details.
+
+#ifndef MFEM_DARCYOP
+#define MFEM_DARCYOP
+
+#include "mfem.hpp"
+#include "../general/socketstream.hpp"
+
+namespace mfem
+{
+
+class DarcyOperator : public TimeDependentOperator
+{
+public:
+   enum class SolverType
+   {
+      Default = 0,
+      LBFGS,
+      LBB,
+      Newton,
+      KINSol,
+   };
+
+private:
+   Array<int> offsets;
+   const Array<int> &ess_flux_tdofs_list;
+   DarcyForm *darcy;
+   LinearForm *g, *f, *h;
+#ifdef MFEM_USE_MPI
+   ParDarcyForm *pdarcy {};
+   ParLinearForm *pg{}, *pf{}, *ph{};
+#endif
+   const Array<Coefficient*> &coeffs;
+   SolverType solver_type;
+   bool btime_u, btime_p;
+   real_t rtol{1e-6}, atol{1e-10};
+   int max_iters{1000};
+
+   FiniteElementSpace *trace_space{};
+
+   real_t idt{};
+   std::unique_ptr<Coefficient> idtcoeff;
+   std::unique_ptr<BilinearForm> Mt0, Mq0;
+
+   std::string lsolver_str;
+   std::unique_ptr<Solver> prec, lin_prec;
+   std::string prec_str, lin_prec_str;
+   std::unique_ptr<IterativeSolver> solver;
+   std::string solver_str;
+   std::unique_ptr<IterativeSolverMonitor> monitor;
+   int monitor_step{-1};
+
+   mutable BlockVector x, rhs;
+
+   class SchurPreconditioner : public Solver
+   {
+      const DarcyForm *darcy;
+#ifdef MFEM_USE_MPI
+      const ParDarcyForm *pdarcy {};
+#endif
+      const Operator *op {};
+      bool nonlinear;
+
+      const char *prec_str;
+      mutable std::unique_ptr<BlockDiagonalPreconditioner> darcyPrec;
+      mutable std::unique_ptr<SparseMatrix> S;
+#ifdef MFEM_USE_MPI
+      mutable std::unique_ptr<HypreParMatrix> hS;
+#endif
+      mutable bool reconstruct {};
+
+      void Construct(const Vector &x) const;
+#ifdef MFEM_USE_MPI
+      void ConstructPar(const Vector &x) const;
+#endif
+
+   public:
+      SchurPreconditioner(const DarcyForm *darcy, bool nonlinear = false);
+#ifdef MFEM_USE_MPI
+      SchurPreconditioner(const ParDarcyForm *darcy, bool nonlinear = false);
+#endif
+
+      const char *GetString() const { return prec_str; }
+
+      void SetOperator(const Operator &op_) override
+      { op = &op_; reconstruct = true; }
+
+      void Mult(const Vector &x, Vector &y) const override;
+   };
+
+public:
+   class SolutionController : public IterativeSolverController
+   {
+   public:
+      enum class Type
+      {
+         Native,
+         Flux,
+         Potential
+      };
+
+   protected:
+      DarcyForm &darcy;
+      BlockVector &x;
+      const BlockVector &rhs;
+      Type type;
+      real_t rtol;
+      int it_prev{};
+      Vector sol_prev;
+
+      bool CheckSolution(const Vector &x, const Vector &y) const;
+      virtual void ReduceValues(real_t diff[], int num) const { }
+
+   public:
+      SolutionController(DarcyForm &darcy, BlockVector &x, const BlockVector &rhs,
+                         Type type, real_t rtol);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+
+      bool RequiresUpdatedSolution() const override { return true; }
+   };
+
+#ifdef MFEM_USE_MPI
+   class ParSolutionController : public SolutionController
+   {
+   protected:
+      ParDarcyForm &pdarcy;
+
+      void ReduceValues(real_t diff[], int num) const override;
+
+   public:
+      ParSolutionController(ParDarcyForm &pdarcy, BlockVector &x,
+                            const BlockVector &rhs, Type type, real_t rtol);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+   };
+#endif //MFEM_USE_MPI
+
+private:
+   SolutionController::Type sol_type{SolutionController::Type::Native};
+
+   class IterativeGLVis : public IterativeSolverMonitor
+   {
+   protected:
+      DarcyForm &darcy;
+      BlockVector &x;
+      const BlockVector &rhs;
+      int step;
+      bool save_files;
+
+      socketstream q_sock, t_sock;
+
+      virtual void StreamPreamble(socketstream &ss) { }
+      virtual std::string FormFilename(const char *base, int it,
+                                       const char *suff = "gf");
+   public:
+      IterativeGLVis(DarcyForm &darcy, BlockVector &x, const BlockVector &rhs,
+                     int step = 0, bool save_files = false);
+
+      void MonitorSolution(int it, real_t norm, const Vector &x,
+                           bool final) override;
+
+      bool RequiresUpdatedSolution() const override { return true; }
+   };
+
+#ifdef MFEM_USE_MPI
+   class ParIterativeGLVis : public IterativeGLVis
+   {
+      ParDarcyForm &pdarcy;
+
+      void StreamPreamble(socketstream &ss) override;
+      std::string FormFilename(const char *base, int it,
+                               const char *suff = "gf") override;
+   public:
+      ParIterativeGLVis(ParDarcyForm &pdarcy_, BlockVector &x, const BlockVector &rhs,
+                        int step = 0, bool save_files = false)
+         : IterativeGLVis(pdarcy_, x, rhs, step), pdarcy(pdarcy_) { }
+   };
+#endif //MFEM_USE_MPI
+
+   void SetupNonlinearSolver(real_t rtol, real_t atol, int iters);
+   void SetupLinearSolver(real_t rtol, real_t atol, int iters);
+
+public:
+   DarcyOperator(const Array<int> &ess_flux_tdofs_list, DarcyForm *darcy,
+                 LinearForm *g, LinearForm *f, LinearForm *h, const Array<Coefficient*> &coeffs,
+                 SolverType stype = SolverType::LBFGS,  bool bflux_u = true,
+                 bool btime_p = true);
+#ifdef MFEM_USE_MPI
+   DarcyOperator(const Array<int> &ess_flux_tdofs_list, ParDarcyForm *darcy,
+                 ParLinearForm *g, ParLinearForm *f, ParLinearForm *h,
+                 const Array<Coefficient*> &coeffs,
+                 SolverType stype = SolverType::LBFGS,  bool bflux_u = true,
+                 bool btime_p = true);
+#endif
+
+   ~DarcyOperator();
+
+   void SetTolerance(real_t rtol_, real_t atol_ = 0.) { rtol = rtol_; atol = atol_; }
+   void SetMaxIters(int iters_) { max_iters = iters_; }
+
+   void EnableSolutionController(SolutionController::Type type) { sol_type = type; }
+   void EnableIterationsVisualization(int vis_step = 0) { monitor_step = vis_step; }
+
+   static Array<int> ConstructOffsets(const DarcyForm &darcy);
+   inline const Array<int>& GetOffsets() const { return offsets; }
+
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;
+};
+
+void RandomizeMesh(Mesh &mesh, real_t dr);
+
+}
+
+#endif
@@ -27,7 +27,6 @@
 //               ex1 -m ../data/fichera-amr.mesh
 //               ex1 -m ../data/mobius-strip.mesh
 //               ex1 -m ../data/mobius-strip.mesh -o -1 -sc
-//               ex1 -m ../data/nc3-nurbs.mesh -o -1
 //
 // Device sample runs:
 //               ex1 -pa -d cuda
@@ -0,0 +1,605 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system
+//
+//                                 k*u + grad p = f
+//                                 - div u      = g
+//
+//               with natural boundary condition -p = <given pressure>.
+//               Here, we use a given exact solution (u,p) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Raviart-Thomas
+//               finite elements (velocity u) and piecewise discontinuous
+//               polynomials (pressure p). Alternatively, the piecewise discontinuous
+//               polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void uFun_ex(const Vector & x, Vector & u);
+real_t pFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool dg = false;
+   bool brt = false;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool reduction = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&brt, "-brt", "--broken-RT", "-no-brt",
+                  "--no-broken-RT", "Enable broken RT elements for fluxes.");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+                  "--no-reduction", "Enable reduction of DG flux.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll, *R_coll_dg = NULL;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      R_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else if (brt)
+   {
+      R_coll = new BrokenRT_FECollection(order, dim);
+      R_coll_dg = new L2_FECollection(order+1, dim);
+   }
+   else
+   {
+      R_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *R_space_dg = (R_coll_dg)?(new FiniteElementSpace(
+                                                    mesh, R_coll_dg, dim)):(NULL);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k); //acoustic resistance
+   RatioCoefficient ikcoeff(1., kcoeff); //inverse acoustic resistance
+
+   VectorFunctionCoefficient fcoeff(dim, fFun); //velocity rhs
+   FunctionCoefficient fnatcoeff(f_natural); //boundary velocity rhs
+   FunctionCoefficient gcoeff(gFun); //pressure rhs
+
+   VectorFunctionCoefficient ucoeff(dim, uFun_ex); //velocity
+   FunctionCoefficient pcoeff(pFun_ex); //pressure
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction u,p for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (u,p) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      fform->AddDomainIntegrator(new VectorDomainLFIntegrator(fcoeff));
+      fform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   else
+   {
+      fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+      if (brt)
+      {
+         fform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+      }
+      else
+      {
+         fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+      }
+   }
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   BilinearForm *mVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *bVarf = darcy->GetFluxDivForm();
+   BilinearForm *mtVarf = (dg)?(darcy->GetPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      mVarf->AddDomainIntegrator(new VectorMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+      mtVarf->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ikcoeff, td));
+   }
+   else
+   {
+      mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+      if (brt)
+      {
+         bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                             new DGNormalTraceIntegrator(-1.)));
+      }
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+   else if (reduction && (dg || brt))
+   {
+      darcy->EnableFluxReduction();
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization || (reduction && (dg || brt)))
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mVarf->Height());
+         for (int i=0; i<mVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(bVarf->Height());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &B(bVarf->SpMat());
+         MinvBt = Transpose(B);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(B, *MinvBt);
+         if (mtVarf)
+         {
+            SparseMatrix &Mtm(mtVarf->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions u and p. Compute the L2 error norms.
+   GridFunction u, p;
+   if (R_space_dg)
+   {
+      GridFunction u_broken(R_space, x.GetBlock(0), 0);
+      VectorGridFunctionCoefficient coeff(&u_broken);
+      u.SetSpace(R_space_dg);
+      u.ProjectCoefficient(coeff);
+   }
+   else
+   {
+      u.MakeRef(R_space, x.GetBlock(0), 0);
+   }
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeLpNorm(2., pcoeff, *mesh, irs);
+
+   std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+   std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream u_ofs("sol_u.gf");
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs("sol_p.gf");
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock.precision(8);
+      u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream p_sock(vishost, visport);
+      p_sock.precision(8);
+      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+      p_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete R_space_dg;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete R_coll_dg;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+
+void uFun_ex(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   u(0) = - exp(xi)*sin(yi)*cos(zi);
+   u(1) = - exp(xi)*cos(yi)*cos(zi);
+
+   if (x.Size() == 3)
+   {
+      u(2) = exp(xi)*sin(yi)*sin(zi);
+   }
+}
+
+// Change if needed
+real_t pFun_ex(const Vector & x)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return exp(xi)*sin(yi)*cos(zi);
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   f = 0.0;
+}
+
+real_t gFun(const Vector & x)
+{
+   if (x.Size() == 3)
+   {
+      return -pFun_ex(x);
+   }
+   else
+   {
+      return 0;
+   }
+}
+
+real_t f_natural(const Vector & x)
+{
+   return (-pFun_ex(x));
+}
@@ -0,0 +1,634 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D asymptotic heat diffusion
+//               problem in the mixed formulation corresponding to the system
+//
+//                                 k^-1.q + grad T =  f
+//                                  div q +    a*T = -g
+//
+//               with natural boundary condition q.n = 0, where n is the outer
+//               normal. The tensor k represents the heat conductivity, where its
+//               symmetric and antisymmetric parts can be adjusted. The scalar a
+//               is then the heat capacity, which can be zero, changing the problem
+//               to steady-state, indefinite, saddle-point. The r.h.s. is f = 0 and
+//               g = -a * <initial temperature> for the definite problem and
+//               g = -<initial temperature> for the indefinite one. As a reference,
+//               we use the exact solution (q,T) for the asymptote a -> infinity.
+//               We discretize with Raviart-Thomas finite elements (heat flux q)
+//               and piecewise discontinuous polynomials (temperature T). Alternatively,
+//               the piecewise discontinuous polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+typedef std::function<real_t(const Vector &, real_t t)> TDFunc;
+typedef std::function<void(const Vector &, Vector &)> VecFunc;
+typedef std::function<void(const Vector &, DenseMatrix &)> MatFunc;
+
+TDFunc GetTFun(real_t t_0, real_t a, const MatFunc &kFun);
+VecFunc GetQFun(real_t t_0, real_t a, const MatFunc &kFun);
+MatFunc GetKFun(real_t k, real_t ks, real_t ka);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool dg = false;
+   real_t ks = 1.;
+   real_t ka = 0.;
+   real_t a = 0.;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&ks, "-ks", "--kappa_sym",
+                  "Symmetric anisotropy of the heat conductivity tensor");
+   args.AddOption(&ka, "-ka", "--kappa_anti",
+                  "Antisymmetric anisotropy of the heat conductivity tensor");
+   args.AddOption(&a, "-a", "--heat_capacity",
+                  "Heat capacity coefficient (0=indefinite problem)");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *V_coll;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      V_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else
+   {
+      V_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   FiniteElementSpace *V_space = new FiniteElementSpace(mesh, V_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(V_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   const real_t t_0 = 1.; //base temperature
+   const real_t k = 1.; //base heat conductivity
+
+   ConstantCoefficient acoeff(a); //heat capacity
+
+   auto kFun = GetKFun(k, ks, ka);
+   MatrixFunctionCoefficient kcoeff(dim, kFun); //tensor conductivity
+   InverseMatrixCoefficient ikcoeff(kcoeff); //inverse tensor conductivity
+
+   auto tFun = GetTFun(t_0, a, kFun);
+   FunctionCoefficient tcoeff(tFun); //temperature
+   SumCoefficient gcoeff(0, tcoeff, 1., //boundary heat flux rhs
+                         -((a>0.)?(a):(1.)));//<-- due to symmetrization, the sign is opposite
+
+   auto qFun = GetQFun(t_0, a, kFun);
+   VectorFunctionCoefficient qcoeff(dim, qFun); //heat flux
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction q,t for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (q,t) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(V_space, rhs.GetBlock(0), 0);
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   /*Vector v ({-1., 0.});
+   VectorConstantCoefficient vc(v);
+   ConstantCoefficient one;
+   gform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, vc, 1.));*/
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   q_h, v_h \in V_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   q_h \in V_h, w_h \in W_h
+   BilinearForm *Mq = darcy->GetFluxMassForm();
+   MixedBilinearForm *B = darcy->GetFluxDivForm();
+   BilinearForm *Mt = (a > 0. || dg)?(darcy->GetPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      Mq->AddDomainIntegrator(new VectorMassIntegrator(ikcoeff));
+      B->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      B->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                      new DGNormalTraceIntegrator(-1.)));
+      if (td > 0.)
+      {
+         Mt->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(kcoeff, td));
+      }
+   }
+   else
+   {
+      Mq->AddDomainIntegrator(new VectorFEMassIntegrator(ikcoeff));
+      B->AddDomainIntegrator(new VectorFEDivergenceIntegrator());
+   }
+
+   if (Mt)
+   {
+      Mt->AddDomainIntegrator(new MassIntegrator(acoeff));
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+   /*Array<int> bdr_is_ess(mesh->bdr_attributes.Max());
+   bdr_is_ess = 0;
+   bdr_is_ess[3] = -1;
+   V_space->GetEssentialTrueDofs(bdr_is_ess, ess_flux_tdofs_list);*/
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, RHS;
+   //x = 1./ny;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, RHS);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization)
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     temperature Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(Mq->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         Mq->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(Mq->Height());
+         for (int i=0; i<Mq->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(B->Height());
+         B->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &Mqm(Mq->SpMat());
+         Mqm.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &Bm(B->SpMat());
+         MinvBt = Transpose(Bm);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(Bm, *MinvBt);
+         if (Mt)
+         {
+            SparseMatrix &Mtm(Mt->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(Mqm);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions q and t. Compute the L2 error norms.
+   GridFunction q, t;
+   q.MakeRef(V_space, x.GetBlock(0), 0);
+   t.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   qcoeff.SetTime(1.);
+   tcoeff.SetTime(1.);
+
+   real_t err_q  = q.ComputeL2Error(qcoeff, irs);
+   real_t norm_q = ComputeLpNorm(2., qcoeff, *mesh, irs);
+   real_t err_t  = t.ComputeL2Error(tcoeff, irs);
+   real_t norm_t = ComputeLpNorm(2., tcoeff, *mesh, irs);
+
+   std::cout << "|| q_h - q_ex || / || q_ex || = " << err_q / norm_q << "\n";
+   std::cout << "|| t_h - t_ex || / || t_ex || = " << err_t / norm_t << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_q.gf" or "glvis -m ex5.mesh -g
+   //     sol_t.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream q_ofs("sol_q.gf");
+      q_ofs.precision(8);
+      q.Save(q_ofs);
+
+      ofstream t_ofs("sol_t.gf");
+      t_ofs.precision(8);
+      t.Save(t_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("heat flux", &q);
+   visit_dc.RegisterField("temperature", &t);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("heat flux",&q);
+   paraview_dc.RegisterField("temperature",&t);
+   paraview_dc.Save();
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream q_sock(vishost, visport);
+      q_sock.precision(8);
+      q_sock << "solution\n" << *mesh << q << "window_title 'Heat flux'" << endl;
+      q_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream t_sock(vishost, visport);
+      t_sock.precision(8);
+      t_sock << "solution\n" << *mesh << t << "window_title 'Temperature'" << endl;
+      t_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   //delete Mq;
+   //delete B;
+   delete darcy;
+   delete W_space;
+   delete V_space;
+   delete trace_space;
+   delete W_coll;
+   delete V_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+TDFunc GetTFun(real_t t_0, real_t a, const MatFunc &kFun)
+{
+   return [=](const Vector &x, real_t t) -> real_t
+   {
+      const int ndim = x.Size();
+      real_t t0 = t_0 * sin(M_PI*x(0)) * sin(M_PI*x(1));
+      if (ndim > 2)
+      {
+         t0 *= sin(M_PI*x(2));
+      }
+
+      if (a <= 0.) { return t0; }
+
+      Vector ddT((ndim<=2)?(2):(4));
+      ddT(0) = -t_0 * M_PI*M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1));//xx,yy
+      ddT(1) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * cos(M_PI*x(1));//xy
+      if (ndim > 2)
+      {
+         ddT(0) *= sin(M_PI*x(2));//xx,yy,zz
+         ddT(1) *= sin(M_PI*x(2));//xy
+         ddT(2) = +t_0 * M_PI*M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(
+                                                                              2));//xz
+         ddT(3) = +t_0 * M_PI*M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1)) * cos(M_PI*x(
+                                                                              2));//yz
+
+      }
+
+      DenseMatrix kappa;
+      kFun(x, kappa);
+
+      real_t div = -(kappa(0,0) + kappa(1,1)) * ddT(0) - (kappa(0,1) + kappa(1,0)) * ddT(1);
+      if (ndim > 2)
+      {
+         div += -kappa(2,2) * ddT(0) - (kappa(0,2) + kappa(2,0)) * ddT(2) - (kappa(1,
+                                                                                   2) + kappa(2,1)) * ddT(3);
+      }
+      return t0 - div / a * t;
+   };
+}
+
+VecFunc GetQFun(real_t t_0, real_t a, const MatFunc &kFun)
+{
+   return [=](const Vector &x, Vector &v)
+   {
+      const int vdim = x.Size();
+      v.SetSize(vdim);
+
+      Vector gT(vdim);
+      gT = 0.;
+      gT(0) = t_0 * M_PI * cos(M_PI*x(0)) * sin(M_PI*x(1));
+      gT(1) = t_0 * M_PI * sin(M_PI*x(0)) * cos(M_PI*x(1));
+      if (vdim > 2)
+      {
+         gT(0) *= sin(M_PI*x(2));
+         gT(1) *= sin(M_PI*x(2));
+         gT(2) = t_0 * M_PI * sin(M_PI*x(0)) * sin(M_PI*x(1)) * cos(M_PI*x(2));
+      }
+
+      DenseMatrix kappa;
+      kFun(x, kappa);
+
+      if (vdim <= 2)
+      {
+         v(0) = -kappa(0,0) * gT(0) -kappa(0,1) * gT(1);
+         v(1) = -kappa(1,0) * gT(0) -kappa(1,1) * gT(1);
+      }
+      else
+      {
+         kappa.Mult(gT, v);
+         v.Neg();
+      }
+   };
+}
+
+MatFunc GetKFun(real_t k, real_t ks, real_t ka)
+{
+   return [=](const Vector &x, DenseMatrix &kappa)
+   {
+      const int ndim = x.Size();
+      kappa.Diag(k, ndim);
+      kappa(0,0) *= ks;
+      kappa(0,1) = +ka * k;
+      kappa(1,0) = -ka * k;
+      if (ndim > 2)
+      {
+         kappa(0,2) = +ka * k;
+         kappa(2,0) = -ka * k;
+      }
+   };
+}
+
+
@@ -0,0 +1,543 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D mixed electromagnetic
+//               diffusion problem corresponding to the mixed system
+//
+//                                 sigma E - curl B = f
+//                                  curl E +      B = g
+//
+//               with essential boundary condition E x n = <given tangential field>.
+//               Here, we use a given exact solution (E,B) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Nedelec
+//               finite elements (electric field E) and piecewise discontinuous
+//               integral polynomials (magnetic field B).
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as the collective saving of several grid functions in
+//               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void EFun_ex(const Vector & x, Vector & E);
+real_t BFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t freq = 1.0, kappa;
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int order = 1;
+   bool hybridization = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&freq, "-f", "--frequency", "Set the frequency for the exact"
+                  " solution.");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+   kappa = freq * M_PI;
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll(new ND_FECollection(order+1, dim));
+   FiniteElementCollection *W_coll(new L2_FECollection(order, dim, 0,
+                                                       FiniteElement::INTEGRAL));
+
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space);
+
+   // 6. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> &block_offsets = darcy->GetOffsets();
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   std::cout << "dim(R+W) = " << block_offsets.Last() << "\n";
+   std::cout << "***********************************************************\n";
+
+   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
+   ConstantCoefficient muinvsqrt(1.0);
+   ConstantCoefficient sigma(1.0);
+
+   VectorFunctionCoefficient fcoeff(dim, fFun);
+   FunctionCoefficient gcoeff(gFun);
+
+   VectorFunctionCoefficient Ecoeff(dim, EFun_ex);
+   FunctionCoefficient Bcoeff(BFun_ex);
+
+   // 8. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction E,B for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (E,B) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 9. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  C^T ]
+   //                                [ C   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega \sigma E_h \cdot v_h d\Omega   E_h, v_h \in R_h
+   //     C   = \int_\Omega \curl E_h q_h d\Omega   E_h \in R_h, q_h \in W_h
+   //BilinearForm *mEVarf(new BilinearForm(R_space));
+   //MixedBilinearForm *cVarf(new MixedBilinearForm(R_space, W_space));
+   BilinearForm *mEVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *cVarf = darcy->GetFluxDivForm();
+   BilinearForm *mBVarf = darcy->GetPotentialMassForm();
+
+   //if (pa) { mEVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   mEVarf->AddDomainIntegrator(new VectorFEMassIntegrator(sigma));
+   //mEVarf->Assemble();
+   //if (!pa) { mEVarf->Finalize(); }
+
+   //if (pa) { cVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   cVarf->AddDomainIntegrator(new MixedScalarCurlIntegrator(muinvsqrt));
+   //cVarf->Assemble();
+   //if (!pa) { cVarf->Finalize(); }
+
+   mBVarf->AddDomainIntegrator(new MassIntegrator());
+
+   //set essential boundary condition
+
+   GridFunction E, B;
+   E.MakeRef(R_space, x.GetBlock(0), 0);
+   B.MakeRef(W_space, x.GetBlock(1), 0);
+
+   Array<int> ess_flux_tdofs_list;
+   if (mesh->bdr_attributes.Size())
+   {
+      Array<int> ess_bdr(mesh->bdr_attributes.Max());
+      ess_bdr = 1;
+      R_space->GetEssentialTrueDofs(ess_bdr, ess_flux_tdofs_list);
+      E.ProjectBdrCoefficientTangent(Ecoeff, ess_bdr);
+   }
+
+   //set hybridization / assembly level
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new ND_Trace_FECollection(order+1, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new TangentTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+   //if (!pa) { darcy->Finalize(); }
+
+   OperatorHandle pDarcyOp;
+   Vector X, RHS;
+
+   //darcy->FormSystemMatrix(ess_flux_tdofs_list, pDarcyOp);
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, RHS);
+
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization)
+   {
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+   }
+   else
+   {
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       C diag(M)^-1 C^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     magnetic field Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mEVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mEVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mEVarf->Height());
+         for (int i=0; i<mEVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(cVarf->Height());
+         cVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mEVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &C(cVarf->SpMat());
+         MinvBt = Transpose(C);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(C, *MinvBt);
+         if (mBVarf)
+         {
+            SparseMatrix &Mtm(mBVarf->SpMat());
+            SparseMatrix *Snew = Add(Mtm, *S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      FGMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(RHS, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
+   }
+
+   // 12. Create the grid functions E and B. Compute the L2 error norms.
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_E  = E.ComputeL2Error(Ecoeff, irs);
+   real_t norm_E = ComputeLpNorm(2., Ecoeff, *mesh, irs);
+   real_t err_B  = B.ComputeL2Error(Bcoeff, irs);
+   real_t norm_B = ComputeLpNorm(2., Bcoeff, *mesh, irs);
+
+   std::cout << "|| E_h - E_ex || / || E_ex || = " << err_E / norm_E << "\n";
+   std::cout << "|| B_h - B_ex || / || B_ex || = " << err_B / norm_B << "\n";
+
+   // 13. Save the mesh and the solution. This output can be viewed later using
+   //     GLVis: "glvis -m ex5.mesh -g sol_u.gf" or "glvis -m ex5.mesh -g
+   //     sol_p.gf".
+   {
+      ofstream mesh_ofs("ex5.mesh");
+      mesh_ofs.precision(8);
+      mesh->Print(mesh_ofs);
+
+      ofstream E_ofs("sol_E.gf");
+      E_ofs.precision(8);
+      E.Save(E_ofs);
+
+      ofstream B_ofs("sol_B.gf");
+      B_ofs.precision(8);
+      B.Save(B_ofs);
+   }
+
+   // 14. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5", mesh);
+   visit_dc.RegisterField("electric field", &E);
+   visit_dc.RegisterField("magnetic field", &B);
+   visit_dc.Save();
+
+   // 15. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5", mesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("electric field",&E);
+   paraview_dc.RegisterField("magnetic field",&B);
+   paraview_dc.Save();
+
+
+   // 16. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream E_sock(vishost, visport);
+      E_sock.precision(8);
+      E_sock << "solution\n" << *mesh << E << "window_title 'Electric field'" << endl;
+      E_sock << "keys Rljvvvvvmmc" << endl;
+      socketstream B_sock(vishost, visport);
+      B_sock.precision(8);
+      B_sock << "solution\n" << *mesh << B << "window_title 'Magnetic field'" << endl;
+      B_sock << "keys Rljmmc" << endl;
+   }
+
+   // 17. Free the used memory.
+   delete fform;
+   delete gform;
+   //delete mEVarf;
+   //delete cVarf;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+
+void EFun_ex(const Vector & x, Vector & E)
+{
+   const int dim = x.Size();
+
+   if (dim == 3)
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(2));
+      E(2) = sin(kappa * x(0));
+   }
+   else
+   {
+      E(0) = sin(kappa * x(1));
+      E(1) = sin(kappa * x(0));
+      if (x.Size() == 3) { E(2) = 0.0; }
+   }
+}
+
+real_t BFun_ex(const Vector & x)
+{
+   return kappa * (-cos(kappa * x(0)) + cos(kappa * x(1)));
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   const int dim = x.Size();
+
+   if (dim == 3)
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(2));
+      f(2) = (1. + kappa * kappa) * sin(kappa * x(0));
+   }
+   else
+   {
+      f(0) = (1. + kappa * kappa) * sin(kappa * x(1));
+      f(1) = (1. + kappa * kappa) * sin(kappa * x(0));
+      if (x.Size() == 3) { f(2) = 0.0; }
+   }
+}
+
+real_t gFun(const Vector & x)
+{
+   return 0.;
+}
@@ -0,0 +1,938 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D coupled Maxwell + compression
+//               wave interaction problem in the mixed formulation corresponding to
+//               the system
+//
+//                                 du/dt + grad n =  sigma0 * n * E
+//                                 div u +  dn/dt = 0
+//                                 dE/dt - curl B = -sigma0 * n * E
+//                                 dB/dt + curl E = 0
+//
+//               with natural boundary condition n = <given density> and/or
+//               essential (RT) / natural (DG) boundary condition u.n = <given
+//               velocity>. Similarly, essential boundary condition Exnxn =
+//               <given electric field> can be set or natural boundary condition
+//               for the magnetic field. Multiple problems are offered:
+//               1) material wave - compression wave in medium (left u b.c.)
+//               2) Maxwell - electromagnetic wave (left E b.c.)
+//               3) excitation - electromagnetic wave exciting the medium (left
+//                               E b.c.)
+//               4) scaterring - interaction of electromagnetic and compression
+//                               Gaussian beams (bottom u and left E b.c.)
+//               The waves are harmonic in time with the given frequency. We
+//               discretize the problem with normally continuous or broken
+//               Raviart-Thomas, or piecewise discontinuous finite elements the
+//               velocity u; piecewise discontinuous polynomials the density n;
+//               tangentially continuous Nedelec the electric field; and
+//               piecewise discountinuous polynomials the magnetic field B.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include "coupledop.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+typedef std::function<real_t(const Vector &, real_t)> TFunc;
+typedef std::function<void(const Vector &, Vector &)> VecFunc;
+typedef std::function<void(const Vector &, real_t, Vector &)> VecTFunc;
+typedef std::function<real_t(real_t f, const Vector &x)> KFunc;
+
+enum Problem
+{
+   MaterialWave = 1,
+   Maxwell,
+   Excitation,
+   Scattering,
+};
+
+constexpr real_t epsilon = numeric_limits<real_t>::epsilon();
+
+TFunc GetSigFun(Problem prob, real_t f, real_t s0);
+TFunc GetNFun(Problem prob, real_t t_0, real_t k, real_t c);
+VecTFunc GetUFun(Problem prob, real_t f, real_t a0);
+VecTFunc GetEFun(Problem prob, real_t f);
+TFunc GetFFun(Problem prob, real_t t_0, real_t k, real_t c);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   real_t sx = 1.;
+   real_t sy = 1.;
+   int order = 1;
+   bool dg = false;
+   bool brt = false;
+   int iproblem = Problem::MaterialWave;
+   real_t tf = 1.;
+   int nt = 0;
+   int ode = 1;
+   real_t k = 1.;
+   real_t c = 1.;
+   real_t freq = 1.;
+   real_t s0 = 1.;
+   real_t a0 = 1e-3;
+   real_t td = 0.5;
+   bool bc_neumann = false;
+   //bool reduction = false;
+   bool hybridization = false;
+   /*bool nonlinear = false;
+   bool nonlinear_conv = false;
+   bool nonlinear_diff = false;
+   int hdg_scheme = 1;
+   int solver_type = (int)DarcyOperator::SolverType::Default;
+   bool pa = false;*/
+   const char *device_config = "cpu";
+   bool mfem = false;
+   bool visit = false;
+   bool paraview = false;
+   bool visualization = true;
+   bool analytic = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&sx, "-sx", "--size-x",
+                  "Size along x axis.");
+   args.AddOption(&sy, "-sy", "--size-y",
+                  "Size along y axis.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&brt, "-brt", "--broken-RT", "-no-brt",
+                  "--no-broken-RT", "Enable broken RT elements for fluxes.");
+   args.AddOption(&iproblem, "-p", "--problem",
+                  "Problem to solve:\n\t\t"
+                  "1=dumping\n\t\t"
+                  "2=Maxwell\n\t\t");
+   args.AddOption(&tf, "-tf", "--time-final",
+                  "Final time.");
+   args.AddOption(&nt, "-nt", "--ntimesteps",
+                  "Number of time steps.");
+   args.AddOption(&ode, "-ode", "--ode-solver",
+                  "ODE time solver (1=Bacward Euler, 2=RK23L, 3=RK23A, 4=RK34).");
+   args.AddOption(&k, "-k", "--kappa",
+                  "Heat conductivity");
+   args.AddOption(&c, "-c", "--velocity",
+                  "Convection velocity");
+   args.AddOption(&freq, "-f", "--frequency",
+                  "Harmonic frequency");
+   args.AddOption(&s0, "-s0", "--sigma0",
+                  "Coupling factor");
+   args.AddOption(&a0, "-a0", "--amplitude0",
+                  "Amplitude factor");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&bc_neumann, "-bcn", "--bc-neumann", "-no-bcn",
+                  "--no-bc-neumann", "Enable Neumann outflow boundary condition.");
+   //args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+   //               "--no-reduction", "Enable reduction.");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   /*args.AddOption(&nonlinear, "-nl", "--nonlinear", "-no-nl",
+                  "--no-nonlinear", "Enable non-linear regime.");
+   args.AddOption(&nonlinear_conv, "-nlc", "--nonlinear-convection", "-no-nlc",
+                  "--no-nonlinear-convection", "Enable non-linear convection regime.");
+   args.AddOption(&nonlinear_diff, "-nld", "--nonlinear-diffusion", "-no-nld",
+                  "--no-nonlinear-diffusion", "Enable non-linear diffusion regime.");
+   args.AddOption(&hdg_scheme, "-hdg", "--hdg_scheme",
+                  "HDG scheme (1=HDG-I, 2=HDG-II, 3=Rusanov, 4=Godunov).");
+   args.AddOption(&solver_type, "-nls", "--nonlinear-solver",
+                  "Nonlinear solver type (1=LBFGS, 2=LBB, 3=Newton, 4=KINSol).");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");*/
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&mfem, "-mfem", "--mfem", "-no-mfem",
+                  "--no-mfem",
+                  "Enable or disable MFEM output.");
+   args.AddOption(&visit, "-visit", "--visit", "-no-visit",
+                  "--no-visit",
+                  "Enable or disable Visit output.");
+   args.AddOption(&paraview, "-paraview", "--paraview", "-no-paraview",
+                  "--no-paraview",
+                  "Enable or disable ParaView output.");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&analytic, "-anal", "--analytic", "-no-anal",
+                  "--no-analytic",
+                  "Enable or disable analytic solution.");
+
+   args.Parse();
+   if (!args.Good())
+   {
+      args.PrintUsage(cout);
+      return 1;
+   }
+   args.PrintOptions(cout);
+
+   // Set the problem options
+   Problem problem = (Problem)iproblem;
+   bool btime = false;
+   switch (problem)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+      case Problem::Scattering:
+         btime = true;
+         break;
+      default:
+         cerr << "Unknown problem" << endl;
+         return 1;
+   }
+
+   /*if (bnldiff && reduction)
+   {
+      cerr << "Reduction is not possible with non-linear diffusion" << endl;
+      return 1;
+   }
+
+   if (!bconv && !bnlconv && upwinded)
+   {
+      cerr << "Upwinded scheme cannot work without advection" << endl;
+      return 1;
+   }
+
+   if (bnlconv && !nonlinear)
+   {
+      cerr << "Nonlinear convection can only work in the nonlinear regime" << endl;
+      return 1;
+   }*/
+
+   if (btime && nt <= 0)
+   {
+      cerr << "You must specify the number of time steps for time evolving problems"
+           << endl;
+      return 1;
+   }
+
+   // 2. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   device.Print();
+
+   // 3. Read the mesh from the given mesh file. We can handle triangular,
+   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
+   //    the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL, false,
+                                            sx, sy));
+   }
+
+   int dim = mesh->Dimension();
+
+   // Mark boundary conditions
+   Array<int> bdr_u_is_dirichlet(mesh->bdr_attributes.Max());
+   Array<int> bdr_u_is_neumann(bdr_u_is_dirichlet.Size());
+   Array<int> bdr_E_is_neumann(bdr_u_is_dirichlet.Size());
+   bdr_u_is_dirichlet = 0;
+   bdr_u_is_neumann = 0;
+   bdr_E_is_neumann = 0;
+
+   switch (problem)
+   {
+      case Problem::MaterialWave:
+         bdr_u_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_u_is_neumann[0] = -1;//outflow
+            bdr_u_is_neumann[2] = -1;//outflow
+         }
+         break;
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         bdr_u_is_dirichlet = -1;
+         bdr_u_is_neumann[3] = -1;
+         bdr_E_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_E_is_neumann[0] = -1;//outflow
+            bdr_E_is_neumann[2] = -1;//outflow
+         }
+         break;
+      case Problem::Scattering:
+         bdr_u_is_dirichlet = -1;
+         bdr_u_is_neumann[0] = -1;//inflow
+         bdr_E_is_neumann[3] = -1;//inflow
+         if (bc_neumann)
+         {
+            bdr_u_is_neumann[1] = -1;//outflow
+            bdr_u_is_neumann[3] = -1;//outflow
+            bdr_E_is_neumann[0] = -1;//outflow
+            bdr_E_is_neumann[2] = -1;//outflow
+         }
+         break;
+   }
+
+   // 4. Refine the mesh to increase the resolution. In this example we do
+   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
+   //    largest number that gives a final mesh with no more than 10,000
+   //    elements.
+   if (strlen(mesh_file) > 0)
+   {
+      int ref_levels =
+         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 5. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *V_coll, *V_coll_dg = NULL;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      V_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else if (brt)
+   {
+      V_coll = new BrokenRT_FECollection(order, dim);
+      V_coll_dg = new L2_FECollection(order+1, dim);
+   }
+   else
+   {
+      V_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim,
+                                                         BasisType::GaussLobatto);
+   FiniteElementCollection *E_coll = new ND_FECollection(order, dim);
+   FiniteElementCollection *B_coll = new L2_FECollection(order, dim, 0,
+                                                         FiniteElement::INTEGRAL);
+
+   FiniteElementSpace *V_space = new FiniteElementSpace(mesh, V_coll,
+                                                        (dg)?(dim):(1));
+   FiniteElementSpace *V_space_dg = (V_coll_dg)?(new FiniteElementSpace(
+                                                    mesh, V_coll_dg, dim)):(NULL);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+   FiniteElementSpace *E_space = new FiniteElementSpace(mesh, E_coll);
+   FiniteElementSpace *B_space = new FiniteElementSpace(mesh, B_coll);
+
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+   }
+
+   // 6. Define the coefficients, analytical solution, and rhs of the PDE.
+   const real_t t_0 = 1.; //base density
+
+   ConstantCoefficient kcoeff(k); //conductivity
+   ConstantCoefficient ikcoeff(1./k); //inverse conductivity
+
+   auto sigFun = GetSigFun(problem, freq, s0);
+   FunctionCoefficient sigcoeff(sigFun); //coupling
+
+   auto nFun = GetNFun(problem, t_0, k, c);
+   FunctionCoefficient ncoeff(nFun); //density
+   SumCoefficient gcoeff(0., ncoeff, 1., -1.); //boundary velocity rhs
+   ProductCoefficient ghcoeff(0.5, gcoeff);
+
+   auto fFun = GetFFun(problem, t_0, k, c);
+   FunctionCoefficient fcoeff(fFun); //density rhs
+
+   auto uFun = GetUFun(problem, freq, a0);
+   VectorFunctionCoefficient ucoeff(dim, uFun); //velocity
+   ConstantCoefficient one;
+
+   auto Efun = GetEFun(problem, freq);
+   VectorFunctionCoefficient Ecoeff(dim, Efun); //electric field
+
+   // 7. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in V_h
+   //     B   = -\int_\Omega \div u_h u_h d\Omega   u_h \in V_h, w_h \in W_h
+
+   // 8. Define the BlockStructure of the problem, i.e. define the array of
+   //    offsets for each variable. The last component of the Array is the sum
+   //    of the dimensions of each block.
+   const Array<int> block_offsets(CoupledOperator::ConstructOffsets(V_space,
+                                                                    W_space, E_space, B_space, trace_space));
+
+   std::cout << "***********************************************************\n";
+   std::cout << "dim(V) = " << block_offsets[1] - block_offsets[0] << "\n";
+   std::cout << "dim(W) = " << block_offsets[2] - block_offsets[1] << "\n";
+   if (hybridization)
+   {
+      std::cout << "dim(M) = " << block_offsets[3] - block_offsets[2] << "\n";
+      std::cout << "dim(E) = " << block_offsets[4] - block_offsets[3] << "\n";
+      std::cout << "dim(B) = " << block_offsets[5] - block_offsets[4] << "\n";
+      std::cout << "dim(V+W+M+E+B) = " << block_offsets.Last() << "\n";
+   }
+   else
+   {
+      std::cout << "dim(E) = " << block_offsets[3] - block_offsets[2] << "\n";
+      std::cout << "dim(B) = " << block_offsets[4] - block_offsets[3] << "\n";
+      std::cout << "dim(V+W+E+B) = " << block_offsets.Last() << "\n";
+   }
+   std::cout << "***********************************************************\n";
+
+   // 9. Allocate memory (x, rhs) for the analytical solution and the right hand
+   //    side.  Define the GridFunction q,t for the finite element solution and
+   //    linear forms fform and gform for the right hand side.  The data
+   //    allocated by x and rhs are passed as a reference to the grid functions
+   //    (q,t) and the linear forms (fform, gform).
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   x = 0.;
+   GridFunction u_h, n_h, tr_h, E_h, B_h;
+   int i = 0;
+   u_h.MakeRef(V_space, x.GetBlock(i++), 0);
+   n_h.MakeRef(W_space, x.GetBlock(i++), 0);
+   if (trace_space)
+   {
+      tr_h.MakeRef(trace_space, x.GetBlock(i++), 0);
+   }
+   E_h.MakeRef(E_space, x.GetBlock(i++), 0);
+   B_h.MakeRef(B_space, x.GetBlock(i++), 0);
+
+   if (btime)
+   {
+      n_h.ProjectCoefficient(ncoeff); //initial condition
+   }
+
+   if (!dg && !brt)
+   {
+      u_h.ProjectBdrCoefficientNormal(ucoeff,
+                                      bdr_u_is_neumann);   //essential Neumann BC
+   }
+
+   LinearForm *gform(new LinearForm);
+   gform->Update(V_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      gform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(gcoeff),
+                                  bdr_u_is_dirichlet);
+      if (!hybridization)
+      {
+         gform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(
+                                        gcoeff, 0.5), bdr_u_is_neumann);
+      }
+   }
+   else
+   {
+      if (brt)
+      {
+         gform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(gcoeff),
+                                     bdr_u_is_dirichlet);
+         if (!hybridization)
+         {
+            gform->AddBdrFaceIntegrator(new VectorFEBoundaryFluxLFIntegrator(
+                                           ghcoeff), bdr_u_is_neumann);
+         }
+      }
+      else
+      {
+         gform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(gcoeff),
+                                      bdr_u_is_dirichlet);
+      }
+   }
+
+   LinearForm *fform(new LinearForm);
+   fform->Update(W_space, rhs.GetBlock(1), 0);
+   fform->AddDomainIntegrator(new DomainLFIntegrator(fcoeff));
+
+   //Neumann
+   if (!hybridization && (dg || brt))
+   {
+      fform->AddBdrFaceIntegrator(new BoundaryFlowIntegrator(one, ucoeff, +1., 0.),
+                                  bdr_u_is_neumann);
+   }
+
+   //prepare (reduced) solution and rhs vectors
+
+   LinearForm *hform = NULL;
+
+   //Neumann BC for the hybridized system
+
+   if (hybridization)
+   {
+      hform = new LinearForm();
+      hform->Update(trace_space, rhs.GetBlock(2), 0);
+      //note that Neumann BC must be applied only for the velocity
+      //and not the total flux for stability reasons
+      hform->AddBoundaryIntegrator(new BoundaryNormalLFIntegrator(ucoeff, 2),
+                                   bdr_u_is_neumann);
+   }
+
+   //construct the operator
+
+   Array<LinearForm*> lfs({gform, fform, hform, (LinearForm*)NULL, (LinearForm*)NULL});
+
+   Array<Coefficient*> coeffs({(Coefficient*)&gcoeff,
+                               (Coefficient*)&fcoeff,
+                               (Coefficient*)&ucoeff});
+
+   CoupledOperator op(bdr_u_is_neumann, bdr_E_is_neumann, &sigcoeff, lfs, coeffs,
+                      V_space, W_space, E_space, B_space, trace_space, td);
+
+   //construct the time solver
+
+   ODESolver *ode_solver;
+
+   switch (ode)
+   {
+      case 1: ode_solver = new BackwardEulerSolver(); break;
+      case 2: ode_solver = new SDIRK23Solver(2); break;
+      case 3: ode_solver = new SDIRK23Solver(); break;
+      case 4: ode_solver = new SDIRK34Solver(); break;
+      default:
+         MFEM_ABORT("Unknown solver");
+         return 1;
+   }
+
+   ode_solver->Init(op);
+
+   //iterate in time
+
+   if (!btime) { nt = 1; }
+
+   const real_t dt = tf / nt; //time step
+
+   for (int ti = 0; ti < nt; ti++)
+   {
+      //set current time
+
+      real_t t = tf * ti / nt;
+
+      if (!dg && !brt)
+      {
+         ucoeff.SetTime(t);
+         u_h.ProjectBdrCoefficientNormal(ucoeff,
+                                         bdr_u_is_neumann);   //essential Neumann BC
+      }
+
+      Ecoeff.SetTime(t);
+      E_h.ProjectBdrCoefficientTangent(Ecoeff, bdr_E_is_neumann);
+
+      //perform time step
+
+      real_t dt_ = dt;//<---ignore time step changes
+      ode_solver->Step(x, t, dt_);
+
+      // 12. Compute the L2 error norms.
+
+      int order_quad = max(2, 2*order+1);
+      const IntegrationRule *irs[Geometry::NumGeom];
+      for (int i=0; i < Geometry::NumGeom; ++i)
+      {
+         irs[i] = &(IntRules.Get(i, order_quad));
+      }
+
+      real_t err_u  = u_h.ComputeL2Error(ucoeff, irs);
+      real_t norm_u = ComputeLpNorm(2., ucoeff, *mesh, irs);
+      real_t err_n  = n_h.ComputeL2Error(ncoeff, irs);
+      real_t norm_n = ComputeLpNorm(2., ncoeff, *mesh, irs);
+
+      if (btime)
+      {
+         cout << "iter:\t" << ti
+              << "\ttime:\t" << t
+              << "\tq_err:\t" << err_u / norm_u
+              << "\tt_err:\t" << err_n / norm_n
+              << endl;
+      }
+      else
+      {
+         cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+         cout << "|| n_h - n_ex || / || n_ex || = " << err_n / norm_n << "\n";
+      }
+
+      // Project the broken space
+
+      GridFunction u_v;
+      if (V_space_dg)
+      {
+         VectorGridFunctionCoefficient coeff(&u_h);
+         u_v.SetSpace(V_space_dg);
+         u_v.ProjectCoefficient(coeff);
+      }
+      else
+      {
+         u_v.MakeRef(V_space, u_h, 0);
+      }
+
+      // Project the analytic solution
+
+      static GridFunction u_a, n_a, c_gf;
+
+      u_a.SetSpace(V_space);
+      u_a.ProjectCoefficient(ucoeff);
+
+      n_a.SetSpace(W_space);
+      n_a.ProjectCoefficient(ncoeff);
+
+      // 13. Save the mesh and the solution. This output can be viewed later using
+      //     GLVis: "glvis -m ex5.mesh -g sol_q.gf" or "glvis -m ex5.mesh -g
+      //     sol_t.gf".
+      if (mfem)
+      {
+         stringstream ss;
+         ss.str("");
+         ss << "mesh";
+         if (btime) { ss << "_" << ti; }
+         ss << ".mesh";
+         ofstream mesh_ofs(ss.str());
+         mesh_ofs.precision(8);
+         mesh->Print(mesh_ofs);
+
+         ss.str("");
+         ss << "sol_u";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream u_ofs(ss.str());
+         u_ofs.precision(8);
+         u_v.Save(u_ofs);
+
+         ss.str("");
+         ss << "sol_n";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream n_ofs(ss.str());
+         n_ofs.precision(8);
+         n_h.Save(n_ofs);
+
+         ss.str("");
+         ss << "sol_E";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream E_ofs(ss.str());
+         E_ofs.precision(8);
+         E_h.Save(E_ofs);
+
+         ss.str("");
+         ss << "sol_B";
+         if (btime) { ss << "_" << ti; }
+         ss << ".gf";
+         ofstream B_ofs(ss.str());
+         B_ofs.precision(8);
+         B_h.Save(B_ofs);
+      }
+
+      // 14. Save data in the VisIt format
+      if (visit)
+      {
+         static VisItDataCollection visit_dc("Example5", mesh);
+         if (ti == 0)
+         {
+            visit_dc.RegisterField("velocity", &u_h);
+            visit_dc.RegisterField("density", &n_h);
+            if (analytic)
+            {
+               visit_dc.RegisterField("velocity analytic", &u_a);
+               visit_dc.RegisterField("density analytic", &n_a);
+            }
+         }
+         visit_dc.SetCycle(ti);
+         visit_dc.SetTime(t); // set the time
+         visit_dc.Save();
+      }
+
+      // 15. Save data in the ParaView format
+      if (paraview)
+      {
+         static ParaViewDataCollection paraview_dc("Example5", mesh);
+         if (ti == 0)
+         {
+            paraview_dc.SetPrefixPath("ParaView");
+            paraview_dc.SetLevelsOfDetail(order);
+            paraview_dc.SetDataFormat(VTKFormat::BINARY);
+            paraview_dc.SetHighOrderOutput(true);
+            paraview_dc.RegisterField("velocity",&u_h);
+            paraview_dc.RegisterField("density",&n_h);
+            if (analytic)
+            {
+               paraview_dc.RegisterField("velocity analytic", &u_a);
+               paraview_dc.RegisterField("density analytic", &n_a);
+            }
+         }
+         paraview_dc.SetCycle(ti);
+         paraview_dc.SetTime(t); // set the time
+         paraview_dc.Save();
+      }
+
+      // 16. Send the solution by socket to a GLVis server.
+      if (visualization)
+      {
+         const char vishost[] = "localhost";
+         const int  visport   = 19916;
+         static socketstream u_sock(vishost, visport);
+         u_sock.precision(8);
+         u_sock << "solution\n" << *mesh << u_v << endl;
+         if (ti == 0)
+         {
+            u_sock << "window_title 'Velocity'" << endl;
+            u_sock << "keys Rljvvvvvmmc" << endl;
+         }
+         static socketstream n_sock(vishost, visport);
+         n_sock.precision(8);
+         n_sock << "solution\n" << *mesh << n_h << endl;
+         if (ti == 0)
+         {
+            n_sock << "window_title 'Density'" << endl;
+            n_sock << "keys Rljmmc" << endl;
+         }
+         static socketstream E_sock(vishost, visport);
+         E_sock.precision(8);
+         E_sock << "solution\n" << *mesh << E_h << endl;
+         if (ti == 0)
+         {
+            E_sock << "window_title 'Electric field'" << endl;
+            E_sock << "keys Rljvvvvvmmc" << endl;
+         }
+         static socketstream B_sock(vishost, visport);
+         B_sock.precision(8);
+         B_sock << "solution\n" << *mesh << B_h << endl;
+         if (ti == 0)
+         {
+            B_sock << "window_title 'Magnetic field'" << endl;
+            B_sock << "keys Rljmmc" << endl;
+         }
+         if (analytic)
+         {
+            static socketstream qa_sock(vishost, visport);
+            qa_sock.precision(8);
+            qa_sock << "solution\n" << *mesh << u_a << endl;
+            if (ti == 0)
+            {
+               qa_sock << "window_title 'Velocity analytic'" << endl;
+               qa_sock << "keys Rljvvvvvmmc" << endl;
+            }
+            static socketstream ta_sock(vishost, visport);
+            ta_sock.precision(8);
+            ta_sock << "solution\n" << *mesh << n_a << endl;
+            if (ti == 0)
+            {
+               ta_sock << "window_title 'Density analytic'" << endl;
+               ta_sock << "keys Rljmmc" << endl;
+            }
+         }
+      }
+   }
+
+   // 17. Free the used memory.
+
+   delete ode_solver;
+   delete fform;
+   delete gform;
+   delete hform;
+   delete W_space;
+   delete V_space;
+   delete V_space_dg;
+   delete E_space;
+   delete B_space;
+   delete trace_space;
+   delete W_coll;
+   delete V_coll;
+   delete V_coll_dg;
+   delete E_coll;
+   delete B_coll;
+   delete trace_coll;
+   delete mesh;
+
+   return 0;
+}
+
+TFunc GetSigFun(Problem prob, real_t f, real_t s0)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+      case Problem::Excitation:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            constexpr real_t x0 = 0.5;
+            constexpr real_t y0 = 0.5;
+            constexpr real_t w = 0.5;
+            const real_t r = hypot(x(0) - x0, x(1) - y0) / w;
+            return exp(-r*r) * s0;
+         };
+   }
+   return TFunc();
+}
+
+TFunc GetNFun(Problem prob, real_t t_0, real_t k, real_t c)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 1.;
+         };
+   }
+   return TFunc();
+}
+
+VecTFunc GetUFun(Problem prob, real_t f, real_t a0)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.25;
+            constexpr real_t y0 = 0.5;
+            const real_t dy = (x(1) - y0) / w;
+            v(0) = exp(-dy*dy) * sin(M_PI * f * t) * cos(M_PI * x(0));
+         };
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+            v = 0.;
+         };
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.15;
+            constexpr real_t r0 = 0.5;
+            const real_t r = x(0) - r0;
+            const real_t rw = r / w;
+            constexpr real_t zR = 0.5;
+            constexpr real_t z0 = 0.5;
+            const real_t dz = x(1) - z0;
+            const real_t R = dz / (dz*dz + zR*zR);
+            v(1) = exp(-rw*rw) * sin(M_PI * (f * t - r*r / R)) * cos(M_PI * x(1)) * a0;
+         };
+   }
+   return VecTFunc();
+}
+
+VecTFunc GetEFun(Problem prob, real_t f)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.25;
+            constexpr real_t y0 = 0.5;
+            const real_t dy = (x(1) - y0) / w;
+            v(1) = exp(-dy*dy) * sin(M_PI * f * t) * cos(M_PI * x(0));
+         };
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t t, Vector &v)
+         {
+            const int vdim = x.Size();
+            v.SetSize(vdim);
+
+            v = 0.;
+            constexpr real_t w = 0.15;
+            const real_t r = x(1) - 0.5;
+            const real_t rw = r / w;
+            constexpr real_t zR = 0.5;
+            constexpr real_t z0 = 0.5;
+            const real_t dz = x(0) - z0;
+            const real_t R = dz / (dz*dz + zR*zR);
+            v(1) = exp(-rw*rw) * sin(M_PI * (f * t - r*r / R)) * cos(M_PI * x(0));
+         };
+   }
+   return VecTFunc();
+}
+
+TFunc GetFFun(Problem prob, real_t t_0, real_t k, real_t c)
+{
+   switch (prob)
+   {
+      case Problem::MaterialWave:
+      case Problem::Maxwell:
+      case Problem::Excitation:
+      case Problem::Scattering:
+         return [=](const Vector &x, real_t) -> real_t
+         {
+            return 0.;
+         };
+   }
+   return TFunc();
+}
@@ -29,9 +29,10 @@
 //               finite elements (velocity u) and piecewise discontinuous
 //               polynomials (pressure p).
 //
-//               The example demonstrates the use of the BlockOperator class, as
-//               well as the collective saving of several grid functions in
-//               VisIt (visit.llnl.gov) and ParaView (paraview.org) formats.
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
 //
 //               We recommend viewing examples 1-4 before viewing this example.

@@ -55,8 +56,11 @@ int main(int argc, char *argv[])
   StopWatch chrono;

   // 1. Parse command-line options.
-   const char *mesh_file = "../data/star.mesh";
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
   int order = 1;
+   bool hybridization = false;
   bool pa = false;
   const char *device_config = "cpu";
   bool visualization = 1;
@@ -64,8 +68,14 @@ int main(int argc, char *argv[])
   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
                  "--no-partial-assembly", "Enable Partial Assembly.");
   args.AddOption(&device_config, "-d", "--device",
@@ -89,13 +99,28 @@ int main(int argc, char *argv[])
   // 3. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
   //    the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
   int dim = mesh->Dimension();

   // 4. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
   //    largest number that gives a final mesh with no more than 10,000
   //    elements.
+   if (strlen(mesh_file) > 0)
   {
      int ref_levels =
         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
@@ -107,20 +132,23 @@ int main(int argc, char *argv[])

   // 5. Define a finite element space on the mesh. Here we use the
   //    Raviart-Thomas finite elements of the specified order.
-   FiniteElementCollection *hdiv_coll(new RT_FECollection(order, dim));
-   FiniteElementCollection *l2_coll(new L2_FECollection(order, dim));
+   FiniteElementCollection *R_coll(new RT_FECollection(order, dim));
+   FiniteElementCollection *W_coll(new L2_FECollection(order, dim));

-   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, hdiv_coll);
-   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, l2_coll);
+   FiniteElementSpace *R_space = new FiniteElementSpace(mesh, R_coll);
+   FiniteElementSpace *W_space = new FiniteElementSpace(mesh, W_coll);
+
+   DarcyForm *darcy = new DarcyForm(R_space, W_space, false);

   // 6. Define the BlockStructure of the problem, i.e. define the array of
   //    offsets for each variable. The last component of the Array is the sum
   //    of the dimensions of each block.
-   Array<int> block_offsets(3); // number of variables + 1
+   const Array<int> &block_offsets = darcy->GetOffsets();
+   /*(3); // number of variables + 1
   block_offsets[0] = 0;
   block_offsets[1] = R_space->GetVSize();
   block_offsets[2] = W_space->GetVSize();
-   block_offsets.PartialSum();
+   block_offsets.PartialSum();*/

   std::cout << "***********************************************************\n";
   std::cout << "dim(R) = " << block_offsets[1] - block_offsets[0] << "\n";
@@ -129,7 +157,8 @@ int main(int argc, char *argv[])
   std::cout << "***********************************************************\n";

   // 7. Define the coefficients, analytical solution, and rhs of the PDE.
-   ConstantCoefficient k(1.0);
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k);

   VectorFunctionCoefficient fcoeff(dim, fFun);
   FunctionCoefficient fnatcoeff(f_natural);
@@ -167,24 +196,55 @@ int main(int argc, char *argv[])
   //
   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
-   BilinearForm *mVarf(new BilinearForm(R_space));
-   MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
+   //BilinearForm *mVarf(new BilinearForm(R_space));
+   //MixedBilinearForm *bVarf(new MixedBilinearForm(R_space, W_space));
+   BilinearForm *mVarf = darcy->GetFluxMassForm();
+   MixedBilinearForm *bVarf = darcy->GetFluxDivForm();

-   if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(k));
-   mVarf->Assemble();
-   if (!pa) { mVarf->Finalize(); }
+   //if (pa) { mVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+   //mVarf->Assemble();
+   //if (!pa) { mVarf->Finalize(); }

-   if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
-   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
-   bVarf->Assemble();
-   if (!pa) { bVarf->Finalize(); }
+   //if (pa) { bVarf->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+   ConstantCoefficient cdiv(-1.);
+   bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator(cdiv));
+   //bVarf->Assemble();
+   //if (!pa) { bVarf->Finalize(); }

-   BlockOperator darcyOp(block_offsets);
+   //set hybridization / assembly level

-   TransposeOperator *Bt = NULL;
+   Array<int> ess_flux_tdofs_list;
+   /*Array<int> bdr_is_ess(mesh->bdr_attributes.Max());
+   bdr_is_ess = 0;
+   bdr_is_ess[3] = -1;
+   R_space->GetEssentialTrueDofs(bdr_is_ess, ess_flux_tdofs_list);*/

-   if (pa)
+   FiniteElementCollection *trace_coll = NULL;
+   FiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new FiniteElementSpace(mesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+   //if (!pa) { darcy->Finalize(); }
+
+   //BlockOperator darcyOp(block_offsets);
+
+   //TransposeOperator *Bt = NULL;
+
+   /*if (pa)
   {
      Bt = new TransposeOperator(bVarf);

@@ -202,104 +262,163 @@ int main(int argc, char *argv[])
      darcyOp.SetBlock(0,0, &M);
      darcyOp.SetBlock(0,1, Bt);
      darcyOp.SetBlock(1,0, &B);
-   }
+   }*/

-   // 10. Construct the operators for preconditioner
-   //
-   //                 P = [ diag(M)         0         ]
-   //                     [  0       B diag(M)^-1 B^T ]
-   //
-   //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
-   //     pressure Schur Complement
-   SparseMatrix *MinvBt = NULL;
-   Vector Md(mVarf->Height());
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   //darcy->FormSystemMatrix(ess_flux_tdofs_list, pDarcyOp);
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);

-   BlockDiagonalPreconditioner darcyPrec(block_offsets);
-   Solver *invM, *invS;
-   SparseMatrix *S = NULL;
+   chrono.Stop();
+   std::cout << "Assembly took " << chrono.RealTime() << "s.\n";

-   if (pa)
-   {
-      mVarf->AssembleDiagonal(Md);
-      auto Md_host = Md.HostRead();
-      Vector invMd(mVarf->Height());
-      for (int i=0; i<mVarf->Height(); ++i)
-      {
-         invMd(i) = 1.0 / Md_host[i];
-      }

-      Vector BMBt_diag(bVarf->Height());
-      bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
-
-      Array<int> ess_tdof_list;  // empty
-
-      invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
-      invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
-   }
-   else
-   {
-      SparseMatrix &M(mVarf->SpMat());
-      M.GetDiag(Md);
-      Md.HostReadWrite();
-
-      SparseMatrix &B(bVarf->SpMat());
-      MinvBt = Transpose(B);
-
-      for (int i = 0; i < Md.Size(); i++)
-      {
-         MinvBt->ScaleRow(i, 1./Md(i));
-      }
-
-      S = Mult(B, *MinvBt);
-
-      invM = new DSmoother(M);
-
-#ifndef MFEM_USE_SUITESPARSE
-      invS = new GSSmoother(*S);
-#else
-      invS = new UMFPackSolver(*S);
-#endif
-   }
-
-   invM->iterative_mode = false;
-   invS->iterative_mode = false;
-
-   darcyPrec.SetDiagonalBlock(0, invM);
-   darcyPrec.SetDiagonalBlock(1, invS);
-
-   // 11. Solve the linear system with MINRES.
-   //     Check the norm of the unpreconditioned residual.
   int maxIter(1000);
   real_t rtol(1.e-6);
   real_t atol(1.e-10);

-   chrono.Clear();
-   chrono.Start();
-   MINRESSolver solver;
-   solver.SetAbsTol(atol);
-   solver.SetRelTol(rtol);
-   solver.SetMaxIter(maxIter);
-   solver.SetOperator(darcyOp);
-   solver.SetPreconditioner(darcyPrec);
-   solver.SetPrintLevel(1);
-   x = 0.0;
-   solver.Mult(rhs, x);
-   if (device.IsEnabled()) { x.HostRead(); }
-   chrono.Stop();
-
-   if (solver.GetConverged())
+   if (hybridization)
   {
-      std::cout << "MINRES converged in " << solver.GetNumIterations()
-                << " iterations with a residual norm of "
-                << solver.GetFinalNorm() << ".\n";
+      // 10. Construct the preconditioner
+      GSSmoother prec(*pDarcyOp.As<SparseMatrix>());
+
+      // 11. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(prec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "GMRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
   }
   else
   {
-      std::cout << "MINRES did not converge in " << solver.GetNumIterations()
-                << " iterations. Residual norm is " << solver.GetFinalNorm()
-                << ".\n";
+      // 10. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      SparseMatrix *MinvBt = NULL;
+      Vector Md(mVarf->Height());
+
+      BlockDiagonalPreconditioner darcyPrec(block_offsets);
+      Solver *invM, *invS;
+      SparseMatrix *S = NULL;
+
+      if (pa)
+      {
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(mVarf->Height());
+         for (int i=0; i<mVarf->Height(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(bVarf->Height());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         SparseMatrix &M(mVarf->SpMat());
+         M.GetDiag(Md);
+         Md.HostReadWrite();
+
+         SparseMatrix &B(bVarf->SpMat());
+         MinvBt = Transpose(B);
+
+         for (int i = 0; i < Md.Size(); i++)
+         {
+            MinvBt->ScaleRow(i, 1./Md(i));
+         }
+
+         S = Mult(B, *MinvBt);
+
+         invM = new DSmoother(M);
+
+#ifndef MFEM_USE_SUITESPARSE
+         invS = new GSSmoother(*S);
+#else
+         invS = new UMFPackSolver(*S);
+#endif
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 11. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver;
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(1);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (solver.GetConverged())
+      {
+         std::cout << "MINRES converged in " << solver.GetNumIterations()
+                   << " iterations with a residual norm of "
+                   << solver.GetFinalNorm() << ".\n";
+      }
+      else
+      {
+         std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                   << " iterations. Residual norm is " << solver.GetFinalNorm()
+                   << ".\n";
+      }
+      std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+
+      delete invM;
+      delete invS;
+      delete S;
+      //delete Bt;
+      delete MinvBt;
   }
-   std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";

   // 12. Create the grid functions u and p. Compute the L2 error norms.
   GridFunction u, p;
@@ -364,25 +483,25 @@ int main(int argc, char *argv[])
      socketstream u_sock(vishost, visport);
      u_sock.precision(8);
      u_sock << "solution\n" << *mesh << u << "window_title 'Velocity'" << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
      socketstream p_sock(vishost, visport);
      p_sock.precision(8);
      p_sock << "solution\n" << *mesh << p << "window_title 'Pressure'" << endl;
+      p_sock << "keys Rljmmc" << endl;
   }

   // 17. Free the used memory.
   delete fform;
   delete gform;
-   delete invM;
-   delete invS;
-   delete S;
-   delete Bt;
-   delete MinvBt;
-   delete mVarf;
-   delete bVarf;
+   //delete mVarf;
+   //delete bVarf;
+   delete darcy;
   delete W_space;
   delete R_space;
-   delete l2_coll;
-   delete hdiv_coll;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
   delete mesh;

   return 0;
@@ -0,0 +1,655 @@
+//                                MFEM Example 5
+//
+// Compile with: make ex5
+//
+// Sample runs:  ex5 -m ../data/square-disc.mesh
+//               ex5 -m ../data/star.mesh
+//               ex5 -m ../data/star.mesh -pa
+//               ex5 -m ../data/beam-tet.mesh
+//               ex5 -m ../data/beam-hex.mesh
+//               ex5 -m ../data/beam-hex.mesh -pa
+//               ex5 -m ../data/escher.mesh
+//               ex5 -m ../data/fichera.mesh
+//
+// Device sample runs:
+//               ex5 -m ../data/star.mesh -pa -d cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-cuda
+//               ex5 -m ../data/star.mesh -pa -d raja-omp
+//               ex5 -m ../data/beam-hex.mesh -pa -d cuda
+//
+// Description:  This example code solves a simple 2D/3D mixed Darcy problem
+//               corresponding to the saddle point system
+//
+//                                 k*u + grad p = f
+//                                 - div u      = g
+//
+//               with natural boundary condition -p = <given pressure>.
+//               Here, we use a given exact solution (u,p) and compute the
+//               corresponding r.h.s. (f,g).  We discretize with Raviart-Thomas
+//               finite elements (velocity u) and piecewise discontinuous
+//               polynomials (pressure p). Alternatively, the piecewise discontinuous
+//               polynomials are used for both quantities.
+//
+//               The example demonstrates the use of the DarcyForm class, as
+//               well as hybridization of mixed systems and the collective saving
+//               of several grid functions in VisIt (visit.llnl.gov) and ParaView
+//               (paraview.org) formats.
+//
+//               We recommend viewing examples 1-4 before viewing this example.
+
+#include "mfem.hpp"
+#include <fstream>
+#include <iostream>
+#include <algorithm>
+
+using namespace std;
+using namespace mfem;
+
+// Define the analytical solution and forcing terms / boundary conditions
+void uFun_ex(const Vector & x, Vector & u);
+real_t pFun_ex(const Vector & x);
+void fFun(const Vector & x, Vector & f);
+real_t gFun(const Vector & x);
+real_t f_natural(const Vector & x);
+
+int main(int argc, char *argv[])
+{
+   StopWatch chrono;
+
+   // 1. Initialize MPI and HYPRE.
+   Mpi::Init(argc, argv);
+   int num_procs = Mpi::WorldSize();
+   int myid = Mpi::WorldRank();
+   Hypre::Init();
+   bool verbose = (myid == 0);
+
+   // 2. Parse command-line options.
+   const char *mesh_file = "";
+   int nx = 0;
+   int ny = 0;
+   int ref_levels = -1;
+   int order = 1;
+   bool dg = false;
+   real_t td = 0.5;
+   bool hybridization = false;
+   bool reduction = false;
+   bool pa = false;
+   const char *device_config = "cpu";
+   bool visualization = 1;
+   bool par_format = false;
+
+   OptionsParser args(argc, argv);
+   args.AddOption(&mesh_file, "-m", "--mesh",
+                  "Mesh file to use.");
+   args.AddOption(&ref_levels, "-r", "--refine",
+                  "Number of times to refine the mesh uniformly.");
+   args.AddOption(&nx, "-nx", "--ncells-x",
+                  "Number of cells in x.");
+   args.AddOption(&ny, "-ny", "--ncells-y",
+                  "Number of cells in y.");
+   args.AddOption(&order, "-o", "--order",
+                  "Finite element order (polynomial degree).");
+   args.AddOption(&dg, "-dg", "--discontinuous", "-no-dg",
+                  "--no-discontinuous", "Enable DG elements for fluxes.");
+   args.AddOption(&td, "-td", "--stab_diff",
+                  "Diffusion stabilization factor (1/2=default)");
+   args.AddOption(&hybridization, "-hb", "--hybridization", "-no-hb",
+                  "--no-hybridization", "Enable hybridization.");
+   args.AddOption(&reduction, "-rd", "--reduction", "-no-rd",
+                  "--no-reduction", "Enable reduction of DG flux.");
+   args.AddOption(&pa, "-pa", "--partial-assembly", "-no-pa",
+                  "--no-partial-assembly", "Enable Partial Assembly.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
+   args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
+                  "--no-visualization",
+                  "Enable or disable GLVis visualization.");
+   args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
+                  "--serial-format",
+                  "Format to use when saving the results for VisIt.");
+   args.Parse();
+   if (!args.Good())
+   {
+      if (verbose)
+      {
+         args.PrintUsage(cout);
+      }
+      return 1;
+   }
+   if (verbose)
+   {
+      args.PrintOptions(cout);
+   }
+
+   // 3. Enable hardware devices such as GPUs, and programming models such as
+   //    CUDA, OCCA, RAJA and OpenMP based on command line options.
+   Device device(device_config);
+   if (myid == 0) { device.Print(); }
+
+   // 4. Read the (serial) mesh from the given mesh file on all processors.  We
+   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
+   //    and volume meshes with the same code.
+   if (ny <= 0)
+   {
+      ny = nx;
+   }
+
+   Mesh *mesh = NULL;
+   if (strlen(mesh_file) > 0)
+   {
+      mesh = new Mesh(mesh_file, 1, 1);
+   }
+   else
+   {
+      mesh = new Mesh(Mesh::MakeCartesian2D(nx, ny, Element::QUADRILATERAL));
+   }
+
+   int dim = mesh->Dimension();
+
+   // 5. Refine the serial mesh on all processors to increase the resolution. In
+   //    this example we do 'ref_levels' of uniform refinement. We choose
+   //    'ref_levels' to be the largest number that gives a final mesh with no
+   //    more than 10,000 elements, unless the user specifies it as input.
+   if (strlen(mesh_file) > 0)
+   {
+      if (ref_levels == -1)
+      {
+         ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      }
+
+      for (int l = 0; l < ref_levels; l++)
+      {
+         mesh->UniformRefinement();
+      }
+   }
+
+   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   //    this mesh further in parallel to increase the resolution. Once the
+   //    parallel mesh is defined, the serial mesh can be deleted.
+   ParMesh *pmesh = new ParMesh(MPI_COMM_WORLD, *mesh);
+   delete mesh;
+   /*{
+      int par_ref_levels = 2;
+      for (int l = 0; l < par_ref_levels; l++)
+      {
+         pmesh->UniformRefinement();
+      }
+   }*/
+
+   // 7. Define a finite element space on the mesh. Here we use the
+   //    Raviart-Thomas finite elements of the specified order.
+   FiniteElementCollection *R_coll;
+   if (dg)
+   {
+      // In the case of LDG formulation, we chose a closed basis as it
+      // is customary for HDG to match trace DOFs, but an open basis can
+      // be used instead.
+      R_coll = new L2_FECollection(order, dim, BasisType::GaussLobatto);
+   }
+   else
+   {
+      R_coll = new RT_FECollection(order, dim);
+   }
+   FiniteElementCollection *W_coll = new L2_FECollection(order, dim);
+
+   ParFiniteElementSpace *R_space = new ParFiniteElementSpace(pmesh, R_coll,
+                                                              (dg)?(dim):(1));
+   ParFiniteElementSpace *W_space = new ParFiniteElementSpace(pmesh, W_coll);
+
+   ParDarcyForm *darcy = new ParDarcyForm(R_space, W_space);
+
+   HYPRE_BigInt dimR = R_space->GlobalTrueVSize();
+   HYPRE_BigInt dimW = W_space->GlobalTrueVSize();
+
+   if (verbose)
+   {
+      std::cout << "***********************************************************\n";
+      std::cout << "dim(R) = " << dimR << "\n";
+      std::cout << "dim(W) = " << dimW << "\n";
+      std::cout << "dim(R+W) = " << dimR + dimR << "\n";
+      std::cout << "***********************************************************\n";
+   }
+
+   // 8. Define the two BlockStructure of the problem.  block_offsets is used
+   //    for Vector based on dof (like ParGridFunction or ParLinearForm),
+   //    block_trueOffstes is used for Vector based on trueDof (HypreParVector
+   //    for the rhs and solution of the linear system).  The offsets computed
+   //    here are local to the processor.
+
+   const Array<int> &block_offsets = darcy->GetOffsets();
+   const Array<int> &block_trueOffsets = darcy->GetTrueOffsets();
+
+   // 9. Define the coefficients, analytical solution, and rhs of the PDE.
+   const double k = 1.0;
+   ConstantCoefficient kcoeff(k); //acoustic resistance
+   RatioCoefficient ikcoeff(1., kcoeff); //inverse acoustic resistance
+
+   VectorFunctionCoefficient fcoeff(dim, fFun); //velocity rhs
+   FunctionCoefficient fnatcoeff(f_natural); //boundary velocity rhs
+   FunctionCoefficient gcoeff(gFun); //pressure rhs
+
+   VectorFunctionCoefficient ucoeff(dim, uFun_ex); //velocity
+   FunctionCoefficient pcoeff(pFun_ex); //pressure
+
+   // 10. Define the parallel grid function and parallel linear forms, solution
+   //     vector and rhs.
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+
+   ParLinearForm *fform(new ParLinearForm);
+   fform->Update(R_space, rhs.GetBlock(0), 0);
+   if (dg)
+   {
+      fform->AddDomainIntegrator(new VectorDomainLFIntegrator(fcoeff));
+      fform->AddBdrFaceIntegrator(new VectorBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   else
+   {
+      fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
+      fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
+   }
+   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
+
+   ParLinearForm *gform(new ParLinearForm);
+   gform->Update(W_space, rhs.GetBlock(1), 0);
+   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
+   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
+
+   // 11. Assemble the finite element matrices for the Darcy operator
+   //
+   //                            D = [ M  B^T ]
+   //                                [ B   0  ]
+   //     where:
+   //
+   //     M = \int_\Omega k u_h \cdot v_h d\Omega   u_h, v_h \in R_h
+   //     B   = -\int_\Omega \div u_h q_h d\Omega   u_h \in R_h, q_h \in W_h
+   ParBilinearForm *mVarf = darcy->GetParFluxMassForm();
+   ParMixedBilinearForm *bVarf = darcy->GetParFluxDivForm();
+   ParBilinearForm *mtVarf = (dg)?(darcy->GetParPotentialMassForm()):(NULL);
+
+   if (dg)
+   {
+      mVarf->AddDomainIntegrator(new VectorMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorDivergenceIntegrator());
+      bVarf->AddInteriorFaceIntegrator(new TransposeIntegrator(
+                                          new DGNormalTraceIntegrator(-1.)));
+      mtVarf->AddInteriorFaceIntegrator(new HDGDiffusionIntegrator(ikcoeff, td));
+   }
+   else
+   {
+      mVarf->AddDomainIntegrator(new VectorFEMassIntegrator(kcoeff));
+      bVarf->AddDomainIntegrator(new VectorFEDivergenceIntegrator);
+   }
+
+   //set hybridization / assembly level
+
+   Array<int> ess_flux_tdofs_list;
+
+   FiniteElementCollection *trace_coll = NULL;
+   ParFiniteElementSpace *trace_space = NULL;
+
+   chrono.Clear();
+   chrono.Start();
+
+   if (hybridization)
+   {
+      trace_coll = new DG_Interface_FECollection(order, dim);
+      trace_space = new ParFiniteElementSpace(pmesh, trace_coll);
+      darcy->EnableHybridization(trace_space,
+                                 new NormalTraceJumpIntegrator(),
+                                 ess_flux_tdofs_list);
+   }
+   else if (reduction && dg)
+   {
+      darcy->EnableFluxReduction();
+   }
+
+   if (pa) { darcy->SetAssemblyLevel(AssemblyLevel::PARTIAL); }
+
+   darcy->Assemble();
+
+   OperatorHandle pDarcyOp;
+   Vector X, B;
+   x = 0.;
+   darcy->FormLinearSystem(ess_flux_tdofs_list, x, rhs,
+                           pDarcyOp, X, B);
+
+   chrono.Stop();
+   if (verbose)
+   {
+      std::cout << "Assembly took " << chrono.RealTime() << "s.\n";
+   }
+
+
+   int maxIter(1000);
+   real_t rtol(1.e-6);
+   real_t atol(1.e-10);
+
+   if (hybridization || (reduction && dg))
+   {
+      // 12. Construct the preconditioner
+      HypreBoomerAMG prec;
+
+      // 13. Solve the linear system with GMRES.
+      //     Check the norm of the unpreconditioned residual.
+      chrono.Clear();
+      chrono.Start();
+      GMRESSolver solver(MPI_COMM_WORLD);
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetPreconditioner(prec);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPrintLevel(verbose);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      chrono.Stop();
+
+      if (verbose)
+      {
+         if (solver.GetConverged())
+         {
+            std::cout << "GMRES converged in " << solver.GetNumIterations()
+                      << " iterations with a residual norm of "
+                      << solver.GetFinalNorm() << ".\n";
+         }
+         else
+         {
+            std::cout << "GMRES did not converge in " << solver.GetNumIterations()
+                      << " iterations. Residual norm is " << solver.GetFinalNorm()
+                      << ".\n";
+         }
+         std::cout << "GMRES solver took " << chrono.RealTime() << "s.\n";
+      }
+   }
+   else
+   {
+      // 12. Construct the operators for preconditioner
+      //
+      //                 P = [ diag(M)         0         ]
+      //                     [  0       B diag(M)^-1 B^T ]
+      //
+      //     Here we use Symmetric Gauss-Seidel to approximate the inverse of the
+      //     pressure Schur Complement
+      HypreParMatrix *MinvBt = NULL;
+      HypreParVector *Md = NULL;
+      HypreParMatrix *S = NULL;
+      Solver *invM, *invS;
+
+      if (pa)
+      {
+         Vector Md(R_space->GetTrueVSize());
+         mVarf->AssembleDiagonal(Md);
+         auto Md_host = Md.HostRead();
+         Vector invMd(Md.Size());
+         for (int i=0; i<Md.Size(); ++i)
+         {
+            invMd(i) = 1.0 / Md_host[i];
+         }
+
+         Vector BMBt_diag(W_space->GetTrueVSize());
+         bVarf->AssembleDiagonal_ADAt(invMd, BMBt_diag);
+
+         Array<int> ess_tdof_list;  // empty
+
+         invM = new OperatorJacobiSmoother(Md, ess_tdof_list);
+         invS = new OperatorJacobiSmoother(BMBt_diag, ess_tdof_list);
+      }
+      else
+      {
+         HypreParMatrix &M = *mVarf->ParallelAssembleInternal();
+         Md = new HypreParVector(MPI_COMM_WORLD, M.GetGlobalNumRows(),
+                                 M.GetRowStarts());
+         M.GetDiag(*Md);
+
+         HypreParMatrix &B = *bVarf->ParallelAssembleInternal();
+         MinvBt = B.Transpose();
+         MinvBt->InvScaleRows(*Md);
+         S = ParMult(&B, MinvBt);
+
+         if (mtVarf)
+         {
+            HypreParMatrix &Mt = *mtVarf->ParallelAssembleInternal();
+            HypreParMatrix *Snew = ParAdd(&Mt, S);
+            delete S;
+            S = Snew;
+         }
+
+         invM = new HypreDiagScale(M);
+         invS = new HypreBoomerAMG(*S);
+      }
+
+      invM->iterative_mode = false;
+      invS->iterative_mode = false;
+
+      BlockDiagonalPreconditioner darcyPrec(block_trueOffsets);
+      darcyPrec.SetDiagonalBlock(0, invM);
+      darcyPrec.SetDiagonalBlock(1, invS);
+
+      // 13. Solve the linear system with MINRES.
+      //     Check the norm of the unpreconditioned residual.
+
+      chrono.Clear();
+      chrono.Start();
+      MINRESSolver solver(MPI_COMM_WORLD);
+      solver.SetAbsTol(atol);
+      solver.SetRelTol(rtol);
+      solver.SetMaxIter(maxIter);
+      solver.SetOperator(*pDarcyOp);
+      solver.SetPreconditioner(darcyPrec);
+      solver.SetPrintLevel(verbose);
+
+      solver.Mult(B, X);
+      darcy->RecoverFEMSolution(X, rhs, x);
+
+      if (device.IsEnabled()) { x.HostRead(); }
+      chrono.Stop();
+
+      if (verbose)
+      {
+         if (solver.GetConverged())
+         {
+            std::cout << "MINRES converged in " << solver.GetNumIterations()
+                      << " iterations with a residual norm of "
+                      << solver.GetFinalNorm() << ".\n";
+         }
+         else
+         {
+            std::cout << "MINRES did not converge in " << solver.GetNumIterations()
+                      << " iterations. Residual norm is " << solver.GetFinalNorm()
+                      << ".\n";
+         }
+         std::cout << "MINRES solver took " << chrono.RealTime() << "s.\n";
+      }
+
+      delete invM;
+      delete invS;
+      delete S;
+      delete Md;
+      delete MinvBt;
+   }
+
+   // 14. Extract the parallel grid function corresponding to the finite element
+   //     approximation X. This is the local solution on each processor. Compute
+   //     L2 error norms.
+   ParGridFunction u, p;
+   u.MakeRef(R_space, x.GetBlock(0), 0);
+   p.MakeRef(W_space, x.GetBlock(1), 0);
+
+   int order_quad = max(2, 2*order+1);
+   const IntegrationRule *irs[Geometry::NumGeom];
+   for (int i=0; i < Geometry::NumGeom; ++i)
+   {
+      irs[i] = &(IntRules.Get(i, order_quad));
+   }
+
+   real_t err_u  = u.ComputeL2Error(ucoeff, irs);
+   real_t norm_u = ComputeGlobalLpNorm(2., ucoeff, *pmesh, irs);
+   real_t err_p  = p.ComputeL2Error(pcoeff, irs);
+   real_t norm_p = ComputeGlobalLpNorm(2., pcoeff, *pmesh, irs);
+
+   if (verbose)
+   {
+      std::cout << "|| u_h - u_ex || / || u_ex || = " << err_u / norm_u << "\n";
+      std::cout << "|| p_h - p_ex || / || p_ex || = " << err_p / norm_p << "\n";
+   }
+
+   // 15. Save the refined mesh and the solution in parallel. This output can be
+   //     viewed later using GLVis: "glvis -np <np> -m mesh -g sol_*".
+   {
+      ostringstream mesh_name, u_name, p_name;
+      mesh_name << "mesh." << setfill('0') << setw(6) << myid;
+      u_name << "sol_u." << setfill('0') << setw(6) << myid;
+      p_name << "sol_p." << setfill('0') << setw(6) << myid;
+
+      ofstream mesh_ofs(mesh_name.str().c_str());
+      mesh_ofs.precision(8);
+      pmesh->Print(mesh_ofs);
+
+      ofstream u_ofs(u_name.str().c_str());
+      u_ofs.precision(8);
+      u.Save(u_ofs);
+
+      ofstream p_ofs(p_name.str().c_str());
+      p_ofs.precision(8);
+      p.Save(p_ofs);
+   }
+
+   // 16. Save data in the VisIt format
+   VisItDataCollection visit_dc("Example5-Parallel", pmesh);
+   visit_dc.RegisterField("velocity", &u);
+   visit_dc.RegisterField("pressure", &p);
+   visit_dc.SetFormat(!par_format ?
+                      DataCollection::SERIAL_FORMAT :
+                      DataCollection::PARALLEL_FORMAT);
+   visit_dc.Save();
+
+   // 17. Save data in the ParaView format
+   ParaViewDataCollection paraview_dc("Example5P", pmesh);
+   paraview_dc.SetPrefixPath("ParaView");
+   paraview_dc.SetLevelsOfDetail(order);
+   paraview_dc.SetDataFormat(VTKFormat::BINARY);
+   paraview_dc.SetHighOrderOutput(true);
+   paraview_dc.SetCycle(0);
+   paraview_dc.SetTime(0.0); // set the time
+   paraview_dc.RegisterField("velocity",&u);
+   paraview_dc.RegisterField("pressure",&p);
+   paraview_dc.Save();
+
+   // 18. Optionally output a BP (binary pack) file using ADIOS2. This can be
+   //     visualized with the ParaView VTX reader.
+#ifdef MFEM_USE_ADIOS2
+   if (adios2)
+   {
+      std::string postfix(mesh_file);
+      postfix.erase(0, std::string("../data/").size() );
+      postfix += "_o" + std::to_string(order);
+      const std::string collection_name = "ex5-p_" + postfix + ".bp";
+
+      ADIOS2DataCollection adios2_dc(MPI_COMM_WORLD, collection_name, pmesh);
+      adios2_dc.SetLevelsOfDetail(1);
+      adios2_dc.SetCycle(1);
+      adios2_dc.SetTime(0.0);
+      adios2_dc.RegisterField("velocity",&u);
+      adios2_dc.RegisterField("pressure",&p);
+      adios2_dc.Save();
+   }
+#endif
+
+   // 19. Send the solution by socket to a GLVis server.
+   if (visualization)
+   {
+      char vishost[] = "localhost";
+      int  visport   = 19916;
+      socketstream u_sock(vishost, visport);
+      u_sock << "parallel " << num_procs << " " << myid << "\n";
+      u_sock.precision(8);
+      u_sock << "solution\n" << *pmesh << u << "window_title 'Velocity'"
+             << endl;
+      u_sock << "keys Rljvvvvvmmc" << endl;
+      // Make sure all ranks have sent their 'u' solution before initiating
+      // another set of GLVis connections (one from each rank):
+      MPI_Barrier(pmesh->GetComm());
+      socketstream p_sock(vishost, visport);
+      p_sock << "parallel " << num_procs << " " << myid << "\n";
+      p_sock.precision(8);
+      p_sock << "solution\n" << *pmesh << p << "window_title 'Pressure'"
+             << endl;
+      p_sock << "keys Rljmmc" << endl;
+   }
+
+   // 20. Free the used memory.
+   delete fform;
+   delete gform;
+   delete darcy;
+   delete W_space;
+   delete R_space;
+   delete trace_space;
+   delete W_coll;
+   delete R_coll;
+   delete trace_coll;
+   delete pmesh;
+
+   return 0;
+}
+
+
+void uFun_ex(const Vector & x, Vector & u)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   u(0) = - exp(xi)*sin(yi)*cos(zi);
+   u(1) = - exp(xi)*cos(yi)*cos(zi);
+
+   if (x.Size() == 3)
+   {
+      u(2) = exp(xi)*sin(yi)*sin(zi);
+   }
+}
+
+// Change if needed
+real_t pFun_ex(const Vector & x)
+{
+   real_t xi(x(0));
+   real_t yi(x(1));
+   real_t zi(0.0);
+
+   if (x.Size() == 3)
+   {
+      zi = x(2);
+   }
+
+   return exp(xi)*sin(yi)*cos(zi);
+}
+
+void fFun(const Vector & x, Vector & f)
+{
+   f = 0.0;
+}
+
+real_t gFun(const Vector & x)
+{
+   if (x.Size() == 3)
+   {
+      return -pFun_ex(x);
+   }
+   else
+   {
+      return 0;
+   }
+}
+
+real_t f_natural(const Vector & x)
+{
+   return (-pFun_ex(x));
+}
@@ -20,10 +20,10 @@ CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)

-SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
+SEQ_EXAMPLES = ex0 ex1 ex2 ex3 ex4 ex5 ex5-max ex5-hdg ex5-heat ex6 ex7 ex8 ex9 ex10 ex14 ex15 ex16 \
   ex17 ex18 ex19 ex20 ex21 ex22 ex23 ex24 ex25 ex26 ex27 ex28 ex29 ex30 \
   ex31 ex33 ex34 ex36 ex37 ex38 ex39 ex40
-PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex6p ex7p ex8p ex9p ex10p ex11p \
+PAR_EXAMPLES = ex0p ex1p ex2p ex3p ex4p ex5p ex5p-hdg ex6p ex7p ex8p ex9p ex10p ex11p \
   ex12p ex13p ex14p ex15p ex16p ex17p ex18p ex19p ex20p ex21p ex22p ex24p \
   ex25p ex26p ex27p ex28p ex29p ex30p ex31p ex32p ex33p ex34p ex35p ex36p \
   ex37p ex39p ex40p
@@ -80,10 +80,14 @@ SUBDIRS_TPRINT = $(addsuffix /test-print,$(SUBDIRS))

 # Remove built-in rule
 %: %.cpp
+%.o: %.cpp

 # Replace the default implicit rule for *.cpp files
-%: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
-	$(MFEM_CXX) $(MFEM_FLAGS) $< -o $@ $(MFEM_LIBS)
+%.o: $(SRC)%.cpp $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $< -c -o $@ $(MFEM_LIBS)
+
+%: $(SRC)%.o $(MFEM_LIB_FILE) $(CONFIG_MK)
+	$(MFEM_CXX) $(MFEM_FLAGS) $(filter %.o, $^) -o $@ $(MFEM_LIBS)

 all: $(EXAMPLES) $(SUBDIRS_ALL)

@@ -94,6 +98,11 @@ $(SUBDIRS_TPRINT):
 	@$(MAKE) -C $(@D) $(@F)

 # Additional dependencies
+ex5-nguyen: darcyop.o
+ex5p-nguyen: darcyop.o
+ex5-plasma: darcyop.o
+ex5-aniso: darcyop.o
+ex5-scatter: coupledop.o
 ex18: $(SRC)ex18.hpp
 ex33: $(SRC)ex33.hpp
 ex37: $(SRC)ex37.hpp
@@ -173,12 +182,6 @@ ex11p-test-cpardiso: ex11p
 	@$(call mfem-test,$<, $(RUN_MPI), MKL_CPARDISO example,--cpardiso)
 test-par-YES: ex11p-test-cpardiso
 endif
-ifeq ($(MFEM_USE_CEED),YES)
-ex1p-test-ceed: ex1p
-	@$(call mfem-test,$<, $(RUN_MPI),\
-	   Parallel libCEED example,-d ceed-cpu -pa -a)
-test-par-YES: ex1p-test-ceed
-endif

 # Testing: "test" target and mfem-test* variables are defined in config/test.mk

@@ -16,16 +16,10 @@
 //               multi-physics applications.
 //
 //               This particular example is only for serial runtimes.
-//               For non-conforming meshes please have a look at example
-//               "ex2p.cpp".

 #include "example_utils.hpp"
 #include "mfem.hpp"

-#ifndef MFEM_USE_MOONOLITH
-#error This example requires that MFEM is built with MFEM_USE_MOONOLITH=YES
-#endif
-
 using namespace mfem;
 using namespace std;

@@ -221,8 +215,8 @@ int main(int argc, char *argv[])
         mfem::out << "l2 error: src: " << src_err << ", dest: " << dest_err
                   << std::endl;

-         plot(*src_mesh, src_fun, "source", 0);
-         plot(*dest_mesh, dest_fun, "destination", 1);
+         plot(*src_mesh, src_fun, "source");
+         plot(*dest_mesh, dest_fun, "destination");
      }
   }
   else
@@ -8,23 +8,18 @@
 //   mpirun -np 4 ex1p -s ../../data/inline-hex.mesh -d ../../data/inline-tet.mesh
 //
 // Description:  This example code demonstrates the use of MFEM for transferring
-//               discrete fields from one conforming finite element mesh to another. The
+//               discrete fields from one finite element mesh to another. The
 //               meshes can be of arbitrary shape and completely unrelated with
 //               each other. This feature can be used for implementing immersed
 //               domain methods for fluid-structure interaction or general
 //               multi-physics applications.
 //
 //               This particular example is for parallel runtimes. Vector FE is
-//               an experimental feature in parallel. For non-conforming meshes
-//               please have a look at example "ex2p.cpp".
+//               an experimental feature in parallel.

 #include "example_utils.hpp"
 #include "mfem.hpp"

-#ifndef MFEM_USE_MOONOLITH
-#error This example requires that MFEM is built with MFEM_USE_MOONOLITH=YES
-#endif
-
 using namespace mfem;
 using namespace std;

@@ -55,8 +50,6 @@ int main(int argc, char *argv[])
   int dest_fe_order = 1;
   bool visualization = true;
   bool use_vector_fe = false;
-   bool use_h1 = true;
-   bool use_vector_space = false;
   bool verbose = false;
   bool assemble_mass_and_coupling_together = true;

@@ -79,28 +72,14 @@ int main(int argc, char *argv[])
   args.AddOption(&verbose, "-verb", "--verbose", "--no-verb", "--no-verbose",
                  "Enable/Disable verbose output");
   args.AddOption(&use_vector_fe, "-vfe", "--use_vector_fe", "-no-vfe",
-                  "--no-vector_fe",
-                  "Use RT|ND vector finite elements (Experimental)");
-   args.AddOption(&use_vector_space, "-vfs", "--use_vector_space", "-no-vfs",
-                  "--no-vector_space",
-                  "Use Lagrange vector finite elements (Experimental)");
-   args.AddOption(&use_h1, "-h1", "--use-h1", "-nh1", "--no-h1",
-                  "Use H1 collection");
+                  "--no-vector_fe", "Use vector finite elements (Experimental)");
   args.AddOption(&assemble_mass_and_coupling_together, "-act",
                  "--assemble_mass_and_coupling_together", "-no-act",
                  "--no-assemble_mass_and_coupling_together",
-                  "Assemble mass and coupling operators together (better for "
-                  "non-affine elements)");
+                  "Assemble mass and coupling operators together (better for non-affine elements)");
   args.Parse();
   check_options(args);

-   if (use_vector_fe && use_vector_space)
-   {
-      mfem::err <<
-                "WARNING: use_vector_fe and use_vector_space options"
-                "are both true, ignoring use_vector_fe\n";
-   }
-
   shared_ptr<Mesh> src_mesh, dest_mesh;

   ifstream imesh;
@@ -190,30 +169,17 @@ int main(int argc, char *argv[])
   }
   else
   {
-
-      if (use_h1)
-      {
-         src_fe_coll =
-            make_shared<H1_FECollection>(source_fe_order, src_mesh->Dimension());
-         dest_fe_coll =
-            make_shared<H1_FECollection>(dest_fe_order, dest_mesh->Dimension());
-      }
-      else
-      {
-         src_fe_coll =
-            make_shared<L2_FECollection>(source_fe_order, src_mesh->Dimension());
-         dest_fe_coll =
-            make_shared<L2_FECollection>(dest_fe_order, dest_mesh->Dimension());
-      }
+      src_fe_coll =
+         make_shared<L2_FECollection>(source_fe_order, src_mesh->Dimension());
+      dest_fe_coll =
+         make_shared<L2_FECollection>(dest_fe_order, dest_mesh->Dimension());
   }

-   auto src_fe = make_shared<ParFiniteElementSpace>(
-                    p_src_mesh.get(), src_fe_coll.get(),
-                    use_vector_space ? src_mesh->Dimension() : 1);
+   auto src_fe =
+      make_shared<ParFiniteElementSpace>(p_src_mesh.get(), src_fe_coll.get());

-   auto dest_fe = make_shared<ParFiniteElementSpace>(
-                     p_dest_mesh.get(), dest_fe_coll.get(),
-                     use_vector_space ? dest_mesh->Dimension() : 1);
+   auto dest_fe =
+      make_shared<ParFiniteElementSpace>(p_dest_mesh.get(), dest_fe_coll.get());

   ParGridFunction src_fun(src_fe.get());

@@ -223,7 +189,7 @@ int main(int argc, char *argv[])
   // To be used with vector fe
   VectorFunctionCoefficient vector_coeff(dim, &vector_fun);

-   if (use_vector_fe || use_vector_space)
+   if (use_vector_fe)
   {
      src_fun.ProjectCoefficient(vector_coeff);
      src_fun.Update();
@@ -243,11 +209,7 @@ int main(int argc, char *argv[])
      assemble_mass_and_coupling_together);
   assembler.SetVerbose(verbose);

-   if (use_vector_space)
-   {
-      assembler.AddMortarIntegrator(make_shared<LagrangeVectorL2MortarIntegrator>());
-   }
-   else if (use_vector_fe)
+   if (use_vector_fe)
   {
      assembler.AddMortarIntegrator(make_shared<VectorL2MortarIntegrator>());
   }
@@ -281,8 +243,8 @@ int main(int argc, char *argv[])
                      << std::endl;
         }

-         plot(*p_src_mesh, src_fun, "source", 0);
-         plot(*p_dest_mesh, dest_fun, "destination", 1);
+         plot(*p_src_mesh, src_fun, "source");
+         plot(*p_dest_mesh, dest_fun, "destination");
      }
   }
   else
@@ -20,10 +20,6 @@
 #include "example_utils.hpp"
 #include "mfem.hpp"

-#ifndef MFEM_USE_MOONOLITH
-#error This example requires that MFEM is built with MFEM_USE_MOONOLITH=YES
-#endif
-
 using namespace mfem;
 using namespace std;

@@ -190,8 +186,8 @@ int main(int argc, char *argv[])
                      << std::endl;
         }

-         plot(*p_src_mesh, src_fun, "source", 0);
-         plot(*p_dest_mesh, dest_fun, "destination", 1);
+         plot(*p_src_mesh, src_fun, "source");
+         plot(*p_dest_mesh, dest_fun, "destination");
      }
   }
   else
@@ -84,8 +84,7 @@ void vector_fun(const mfem::Vector &x, mfem::Vector &f)
   f = n;
 }

-inline void plot(mfem::Mesh &mesh, mfem::GridFunction &x, std::string title,
-                 const int plot_number = 0)
+inline void plot(mfem::Mesh &mesh, mfem::GridFunction &x, std::string title)
 {
   using namespace std;
   using namespace mfem;
@@ -104,18 +103,5 @@ inline void plot(mfem::Mesh &mesh, mfem::GridFunction &x, std::string title,
   sol_sock.precision(8);
   sol_sock << "solution\n" << mesh << x
            << "window_title '"<< title << "'\n" << flush;
-
-   sol_sock << "window_geometry ";
-   sol_sock << (plot_number * 600)  << " " << 0 << " " << 600 << " " << 600 <<
-            "\n";
-
-   if (mesh.Dimension() == 2)
-   {
-      sol_sock  << "keys jRmclA\n";
-   }
-   else
-   {
-      sol_sock  << "keys rmclAa\n";
-   }
   sol_sock << flush;
 }
@@ -0,0 +1,117 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --nonlinear
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00966076s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0169918s.
+Preconditioner took 4.6463e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21746, ||r||/||r_0|| = 1.51282
+LBFGS iteration 9 : ||r|| = 0.769563, ||r||/||r_0|| = 0.525019
+LBFGS iteration 10 : ||r|| = 0.607547, ||r||/||r_0|| = 0.414487
+LBFGS iteration 11 : ||r|| = 0.759198, ||r||/||r_0|| = 0.517948
+LBFGS iteration 12 : ||r|| = 1.45778, ||r||/||r_0|| = 0.994541
+LBFGS iteration 13 : ||r|| = 0.563251, ||r||/||r_0|| = 0.384267
+LBFGS iteration 14 : ||r|| = 0.428853, ||r||/||r_0|| = 0.292576
+LBFGS iteration 15 : ||r|| = 0.441501, ||r||/||r_0|| = 0.301206
+LBFGS iteration 16 : ||r|| = 1.38991, ||r||/||r_0|| = 0.948236
+LBFGS iteration 17 : ||r|| = 0.272828, ||r||/||r_0|| = 0.186132
+LBFGS iteration 18 : ||r|| = 0.165047, ||r||/||r_0|| = 0.1126
+LBFGS iteration 19 : ||r|| = 0.151715, ||r||/||r_0|| = 0.103504
+LBFGS iteration 20 : ||r|| = 0.331738, ||r||/||r_0|| = 0.226322
+LBFGS iteration 21 : ||r|| = 0.106159, ||r||/||r_0|| = 0.0724251
+LBFGS iteration 22 : ||r|| = 0.0594514, ||r||/||r_0|| = 0.0405595
+LBFGS iteration 23 : ||r|| = 0.0596277, ||r||/||r_0|| = 0.0406798
+LBFGS iteration 24 : ||r|| = 0.171595, ||r||/||r_0|| = 0.117067
+LBFGS iteration 25 : ||r|| = 0.0533591, ||r||/||r_0|| = 0.0364032
+LBFGS iteration 26 : ||r|| = 0.0273665, ||r||/||r_0|| = 0.0186703
+LBFGS iteration 27 : ||r|| = 0.0191679, ||r||/||r_0|| = 0.013077
+LBFGS iteration 28 : ||r|| = 0.0555099, ||r||/||r_0|| = 0.0378705
+LBFGS iteration 29 : ||r|| = 0.0141599, ||r||/||r_0|| = 0.00966033
+LBFGS iteration 30 : ||r|| = 0.0077165, ||r||/||r_0|| = 0.00526443
+LBFGS iteration 31 : ||r|| = 0.00710641, ||r||/||r_0|| = 0.00484821
+LBFGS iteration 32 : ||r|| = 0.00727829, ||r||/||r_0|| = 0.00496547
+LBFGS iteration 33 : ||r|| = 0.0154916, ||r||/||r_0|| = 0.0105689
+LBFGS iteration 34 : ||r|| = 0.00322952, ||r||/||r_0|| = 0.00220328
+LBFGS iteration 35 : ||r|| = 0.00266012, ||r||/||r_0|| = 0.00181482
+LBFGS iteration 36 : ||r|| = 0.0029587, ||r||/||r_0|| = 0.00201852
+LBFGS iteration 37 : ||r|| = 0.00287213, ||r||/||r_0|| = 0.00195945
+LBFGS iteration 38 : ||r|| = 0.00598566, ||r||/||r_0|| = 0.0040836
+LBFGS iteration 39 : ||r|| = 0.000777973, ||r||/||r_0|| = 0.000530757
+LBFGS iteration 40 : ||r|| = 0.000622731, ||r||/||r_0|| = 0.000424846
+LBFGS iteration 41 : ||r|| = 0.00101354, ||r||/||r_0|| = 0.00069147
+LBFGS iteration 42 : ||r|| = 0.000778935, ||r||/||r_0|| = 0.000531413
+LBFGS iteration 43 : ||r|| = 0.000322145, ||r||/||r_0|| = 0.000219777
+LBFGS iteration 44 : ||r|| = 0.000233689, ||r||/||r_0|| = 0.000159429
+LBFGS iteration 45 : ||r|| = 0.000266598, ||r||/||r_0|| = 0.000181881
+LBFGS iteration 46 : ||r|| = 0.000378973, ||r||/||r_0|| = 0.000258547
+LBFGS iteration 47 : ||r|| = 0.000330508, ||r||/||r_0|| = 0.000225483
+LBFGS iteration 48 : ||r|| = 0.000147423, ||r||/||r_0|| = 0.000100576
+LBFGS iteration 49 : ||r|| = 0.000150309, ||r||/||r_0|| = 0.000102545
+LBFGS iteration 50 : ||r|| = 0.000206405, ||r||/||r_0|| = 0.000140816
+LBFGS iteration 51 : ||r|| = 0.000214436, ||r||/||r_0|| = 0.000146295
+LBFGS iteration 52 : ||r|| = 0.000140579, ||r||/||r_0|| = 9.59076e-05
+LBFGS iteration 53 : ||r|| = 0.000143331, ||r||/||r_0|| = 9.77847e-05
+LBFGS iteration 54 : ||r|| = 0.000184619, ||r||/||r_0|| = 0.000125952
+LBFGS iteration 55 : ||r|| = 8.66031e-05, ||r||/||r_0|| = 5.90832e-05
+LBFGS iteration 56 : ||r|| = 7.3517e-05, ||r||/||r_0|| = 5.01555e-05
+LBFGS iteration 57 : ||r|| = 8.2379e-05, ||r||/||r_0|| = 5.62014e-05
+LBFGS iteration 58 : ||r|| = 0.000205661, ||r||/||r_0|| = 0.000140308
+LBFGS iteration 59 : ||r|| = 6.82689e-05, ||r||/||r_0|| = 4.65751e-05
+LBFGS iteration 60 : ||r|| = 4.65785e-05, ||r||/||r_0|| = 3.17773e-05
+LBFGS iteration 61 : ||r|| = 5.19221e-05, ||r||/||r_0|| = 3.54229e-05
+LBFGS iteration 62 : ||r|| = 0.000121276, ||r||/||r_0|| = 8.27379e-05
+LBFGS iteration 63 : ||r|| = 5.40902e-05, ||r||/||r_0|| = 3.69019e-05
+LBFGS iteration 64 : ||r|| = 3.67227e-05, ||r||/||r_0|| = 2.50533e-05
+LBFGS iteration 65 : ||r|| = 4.11639e-05, ||r||/||r_0|| = 2.80833e-05
+LBFGS iteration 66 : ||r|| = 3.78694e-05, ||r||/||r_0|| = 2.58357e-05
+LBFGS iteration 67 : ||r|| = 0.000192235, ||r||/||r_0|| = 0.000131148
+LBFGS iteration 68 : ||r|| = 1.88491e-05, ||r||/||r_0|| = 1.28594e-05
+LBFGS iteration 69 : ||r|| = 1.37588e-05, ||r||/||r_0|| = 9.38668e-06
+LBFGS iteration 70 : ||r|| = 8.26133e-06, ||r||/||r_0|| = 5.63613e-06
+LBFGS iteration 71 : ||r|| = 1.65205e-05, ||r||/||r_0|| = 1.12708e-05
+LBFGS iteration 72 : ||r|| = 3.0717e-06, ||r||/||r_0|| = 2.09561e-06
+LBFGS iteration 73 : ||r|| = 1.85004e-06, ||r||/||r_0|| = 1.26215e-06
+LBFGS iteration 74 : ||r|| = 1.77343e-06, ||r||/||r_0|| = 1.20989e-06
+LBFGS iteration 75 : ||r|| = 2.89294e-06, ||r||/||r_0|| = 1.97365e-06
+LBFGS iteration 76 : ||r|| = 1.11005e-06, ||r||/||r_0|| = 7.57313e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.11005e-06.
+solver took 3.89622s.
+|| q_h - q_ex || / || q_ex || = 0.000247123
+|| t_h - t_ex || / || t_ex || = 0.000241696
@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.014452s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00999689s.
+Preconditioner took 2.2244e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.21893e-08, ||r||/||r_0|| = 4.24274e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.21893e-08.
+solver took 0.306186s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709
@@ -0,0 +1,124 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.030215s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00968131s.
+Preconditioner took 6.1074e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21745, ||r||/||r_0|| = 1.51281
+LBFGS iteration 9 : ||r|| = 0.769554, ||r||/||r_0|| = 0.525013
+LBFGS iteration 10 : ||r|| = 0.607543, ||r||/||r_0|| = 0.414484
+LBFGS iteration 11 : ||r|| = 0.759138, ||r||/||r_0|| = 0.517907
+LBFGS iteration 12 : ||r|| = 1.4581, ||r||/||r_0|| = 0.994757
+LBFGS iteration 13 : ||r|| = 0.563222, ||r||/||r_0|| = 0.384247
+LBFGS iteration 14 : ||r|| = 0.428817, ||r||/||r_0|| = 0.292552
+LBFGS iteration 15 : ||r|| = 0.44147, ||r||/||r_0|| = 0.301185
+LBFGS iteration 16 : ||r|| = 1.39, ||r||/||r_0|| = 0.9483
+LBFGS iteration 17 : ||r|| = 0.272891, ||r||/||r_0|| = 0.186175
+LBFGS iteration 18 : ||r|| = 0.165054, ||r||/||r_0|| = 0.112605
+LBFGS iteration 19 : ||r|| = 0.151718, ||r||/||r_0|| = 0.103506
+LBFGS iteration 20 : ||r|| = 0.331585, ||r||/||r_0|| = 0.226217
+LBFGS iteration 21 : ||r|| = 0.106143, ||r||/||r_0|| = 0.0724142
+LBFGS iteration 22 : ||r|| = 0.0594506, ||r||/||r_0|| = 0.040559
+LBFGS iteration 23 : ||r|| = 0.0596312, ||r||/||r_0|| = 0.0406822
+LBFGS iteration 24 : ||r|| = 0.171728, ||r||/||r_0|| = 0.117158
+LBFGS iteration 25 : ||r|| = 0.0533533, ||r||/||r_0|| = 0.0363992
+LBFGS iteration 26 : ||r|| = 0.0273829, ||r||/||r_0|| = 0.0186814
+LBFGS iteration 27 : ||r|| = 0.0191745, ||r||/||r_0|| = 0.0130814
+LBFGS iteration 28 : ||r|| = 0.0553769, ||r||/||r_0|| = 0.0377798
+LBFGS iteration 29 : ||r|| = 0.0141317, ||r||/||r_0|| = 0.00964105
+LBFGS iteration 30 : ||r|| = 0.00770544, ||r||/||r_0|| = 0.00525689
+LBFGS iteration 31 : ||r|| = 0.00709767, ||r||/||r_0|| = 0.00484225
+LBFGS iteration 32 : ||r|| = 0.00732886, ||r||/||r_0|| = 0.00499997
+LBFGS iteration 33 : ||r|| = 0.0153653, ||r||/||r_0|| = 0.0104827
+LBFGS iteration 34 : ||r|| = 0.00322618, ||r||/||r_0|| = 0.002201
+LBFGS iteration 35 : ||r|| = 0.00265732, ||r||/||r_0|| = 0.0018129
+LBFGS iteration 36 : ||r|| = 0.00296415, ||r||/||r_0|| = 0.00202224
+LBFGS iteration 37 : ||r|| = 0.00285425, ||r||/||r_0|| = 0.00194726
+LBFGS iteration 38 : ||r|| = 0.00619247, ||r||/||r_0|| = 0.00422469
+LBFGS iteration 39 : ||r|| = 0.000777538, ||r||/||r_0|| = 0.00053046
+LBFGS iteration 40 : ||r|| = 0.000623058, ||r||/||r_0|| = 0.000425069
+LBFGS iteration 41 : ||r|| = 0.00101854, ||r||/||r_0|| = 0.000694876
+LBFGS iteration 42 : ||r|| = 0.000787498, ||r||/||r_0|| = 0.000537255
+LBFGS iteration 43 : ||r|| = 0.000321394, ||r||/||r_0|| = 0.000219265
+LBFGS iteration 44 : ||r|| = 0.000233725, ||r||/||r_0|| = 0.000159455
+LBFGS iteration 45 : ||r|| = 0.000266519, ||r||/||r_0|| = 0.000181828
+LBFGS iteration 46 : ||r|| = 0.000373324, ||r||/||r_0|| = 0.000254693
+LBFGS iteration 47 : ||r|| = 0.000342686, ||r||/||r_0|| = 0.000233791
+LBFGS iteration 48 : ||r|| = 0.00014717, ||r||/||r_0|| = 0.000100404
+LBFGS iteration 49 : ||r|| = 0.000149241, ||r||/||r_0|| = 0.000101817
+LBFGS iteration 50 : ||r|| = 0.000200512, ||r||/||r_0|| = 0.000136795
+LBFGS iteration 51 : ||r|| = 0.000247279, ||r||/||r_0|| = 0.000168701
+LBFGS iteration 52 : ||r|| = 0.000138893, ||r||/||r_0|| = 9.47569e-05
+LBFGS iteration 53 : ||r|| = 0.000129112, ||r||/||r_0|| = 8.80841e-05
+LBFGS iteration 54 : ||r|| = 0.000175704, ||r||/||r_0|| = 0.000119871
+LBFGS iteration 55 : ||r|| = 7.87371e-05, ||r||/||r_0|| = 5.37169e-05
+LBFGS iteration 56 : ||r|| = 7.30606e-05, ||r||/||r_0|| = 4.98442e-05
+LBFGS iteration 57 : ||r|| = 9.5593e-05, ||r||/||r_0|| = 6.52164e-05
+LBFGS iteration 58 : ||r|| = 0.000134289, ||r||/||r_0|| = 9.16163e-05
+LBFGS iteration 59 : ||r|| = 6.66397e-05, ||r||/||r_0|| = 4.54636e-05
+LBFGS iteration 60 : ||r|| = 5.38465e-05, ||r||/||r_0|| = 3.67357e-05
+LBFGS iteration 61 : ||r|| = 5.8085e-05, ||r||/||r_0|| = 3.96274e-05
+LBFGS iteration 62 : ||r|| = 8.23697e-05, ||r||/||r_0|| = 5.61951e-05
+LBFGS iteration 63 : ||r|| = 4.59471e-05, ||r||/||r_0|| = 3.13465e-05
+LBFGS iteration 64 : ||r|| = 4.2169e-05, ||r||/||r_0|| = 2.8769e-05
+LBFGS iteration 65 : ||r|| = 4.36386e-05, ||r||/||r_0|| = 2.97715e-05
+LBFGS iteration 66 : ||r|| = 0.000102276, ||r||/||r_0|| = 6.97757e-05
+LBFGS iteration 67 : ||r|| = 2.55284e-05, ||r||/||r_0|| = 1.74162e-05
+LBFGS iteration 68 : ||r|| = 1.74439e-05, ||r||/||r_0|| = 1.19008e-05
+LBFGS iteration 69 : ||r|| = 1.55022e-05, ||r||/||r_0|| = 1.05761e-05
+LBFGS iteration 70 : ||r|| = 2.78517e-05, ||r||/||r_0|| = 1.90012e-05
+LBFGS iteration 71 : ||r|| = 8.23786e-06, ||r||/||r_0|| = 5.62012e-06
+LBFGS iteration 72 : ||r|| = 3.15803e-06, ||r||/||r_0|| = 2.1545e-06
+LBFGS iteration 73 : ||r|| = 2.32222e-06, ||r||/||r_0|| = 1.58429e-06
+LBFGS iteration 74 : ||r|| = 2.23543e-06, ||r||/||r_0|| = 1.52508e-06
+LBFGS iteration 75 : ||r|| = 6.48079e-06, ||r||/||r_0|| = 4.42139e-06
+LBFGS iteration 76 : ||r|| = 1.24673e-06, ||r||/||r_0|| = 8.50556e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.24673e-06.
+solver took 6.42006s.
+|| q_h - q_ex || / || q_ex || = 0.000247126
+|| t_h - t_ex || / || t_ex || = 0.0002417
@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00849795s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0105149s.
+Preconditioner took 2.9135e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.21638e-08, ||r||/||r_0|| = 4.241e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.21638e-08.
+solver took 0.353555s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709
@@ -0,0 +1,124 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0070498s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0383239s.
+Preconditioner took 5.6454e-05s.
+LBFGS iteration 0 : ||r|| = 1.46578
+LBFGS iteration 1 : ||r|| = 2.01258, ||r||/||r_0|| = 1.37304
+LBFGS iteration 2 : ||r|| = 2.41053, ||r||/||r_0|| = 1.64454
+LBFGS iteration 3 : ||r|| = 4.48418, ||r||/||r_0|| = 3.05924
+LBFGS iteration 4 : ||r|| = 2.44484, ||r||/||r_0|| = 1.66794
+LBFGS iteration 5 : ||r|| = 0.996497, ||r||/||r_0|| = 0.679841
+LBFGS iteration 6 : ||r|| = 0.913284, ||r||/||r_0|| = 0.62307
+LBFGS iteration 7 : ||r|| = 1.03122, ||r||/||r_0|| = 0.703531
+LBFGS iteration 8 : ||r|| = 2.21745, ||r||/||r_0|| = 1.51281
+LBFGS iteration 9 : ||r|| = 0.769554, ||r||/||r_0|| = 0.525013
+LBFGS iteration 10 : ||r|| = 0.607543, ||r||/||r_0|| = 0.414484
+LBFGS iteration 11 : ||r|| = 0.759138, ||r||/||r_0|| = 0.517907
+LBFGS iteration 12 : ||r|| = 1.4581, ||r||/||r_0|| = 0.994757
+LBFGS iteration 13 : ||r|| = 0.563222, ||r||/||r_0|| = 0.384247
+LBFGS iteration 14 : ||r|| = 0.428817, ||r||/||r_0|| = 0.292552
+LBFGS iteration 15 : ||r|| = 0.44147, ||r||/||r_0|| = 0.301185
+LBFGS iteration 16 : ||r|| = 1.39, ||r||/||r_0|| = 0.9483
+LBFGS iteration 17 : ||r|| = 0.272891, ||r||/||r_0|| = 0.186175
+LBFGS iteration 18 : ||r|| = 0.165054, ||r||/||r_0|| = 0.112605
+LBFGS iteration 19 : ||r|| = 0.151718, ||r||/||r_0|| = 0.103506
+LBFGS iteration 20 : ||r|| = 0.331585, ||r||/||r_0|| = 0.226217
+LBFGS iteration 21 : ||r|| = 0.106143, ||r||/||r_0|| = 0.0724142
+LBFGS iteration 22 : ||r|| = 0.0594506, ||r||/||r_0|| = 0.040559
+LBFGS iteration 23 : ||r|| = 0.0596312, ||r||/||r_0|| = 0.0406822
+LBFGS iteration 24 : ||r|| = 0.171728, ||r||/||r_0|| = 0.117158
+LBFGS iteration 25 : ||r|| = 0.0533533, ||r||/||r_0|| = 0.0363992
+LBFGS iteration 26 : ||r|| = 0.0273829, ||r||/||r_0|| = 0.0186814
+LBFGS iteration 27 : ||r|| = 0.0191745, ||r||/||r_0|| = 0.0130814
+LBFGS iteration 28 : ||r|| = 0.0553769, ||r||/||r_0|| = 0.0377798
+LBFGS iteration 29 : ||r|| = 0.0141317, ||r||/||r_0|| = 0.00964106
+LBFGS iteration 30 : ||r|| = 0.00770544, ||r||/||r_0|| = 0.00525689
+LBFGS iteration 31 : ||r|| = 0.00709767, ||r||/||r_0|| = 0.00484225
+LBFGS iteration 32 : ||r|| = 0.00732886, ||r||/||r_0|| = 0.00499997
+LBFGS iteration 33 : ||r|| = 0.0153653, ||r||/||r_0|| = 0.0104827
+LBFGS iteration 34 : ||r|| = 0.00322618, ||r||/||r_0|| = 0.002201
+LBFGS iteration 35 : ||r|| = 0.00265732, ||r||/||r_0|| = 0.00181291
+LBFGS iteration 36 : ||r|| = 0.00296415, ||r||/||r_0|| = 0.00202224
+LBFGS iteration 37 : ||r|| = 0.00285425, ||r||/||r_0|| = 0.00194726
+LBFGS iteration 38 : ||r|| = 0.00619246, ||r||/||r_0|| = 0.00422468
+LBFGS iteration 39 : ||r|| = 0.000777538, ||r||/||r_0|| = 0.00053046
+LBFGS iteration 40 : ||r|| = 0.000623058, ||r||/||r_0|| = 0.000425069
+LBFGS iteration 41 : ||r|| = 0.00101854, ||r||/||r_0|| = 0.000694876
+LBFGS iteration 42 : ||r|| = 0.000787498, ||r||/||r_0|| = 0.000537255
+LBFGS iteration 43 : ||r|| = 0.000321394, ||r||/||r_0|| = 0.000219265
+LBFGS iteration 44 : ||r|| = 0.000233725, ||r||/||r_0|| = 0.000159455
+LBFGS iteration 45 : ||r|| = 0.000266519, ||r||/||r_0|| = 0.000181828
+LBFGS iteration 46 : ||r|| = 0.000373324, ||r||/||r_0|| = 0.000254693
+LBFGS iteration 47 : ||r|| = 0.000342685, ||r||/||r_0|| = 0.00023379
+LBFGS iteration 48 : ||r|| = 0.000147171, ||r||/||r_0|| = 0.000100404
+LBFGS iteration 49 : ||r|| = 0.000149241, ||r||/||r_0|| = 0.000101817
+LBFGS iteration 50 : ||r|| = 0.000200512, ||r||/||r_0|| = 0.000136796
+LBFGS iteration 51 : ||r|| = 0.000247277, ||r||/||r_0|| = 0.0001687
+LBFGS iteration 52 : ||r|| = 0.000138893, ||r||/||r_0|| = 9.4757e-05
+LBFGS iteration 53 : ||r|| = 0.000129112, ||r||/||r_0|| = 8.80844e-05
+LBFGS iteration 54 : ||r|| = 0.000175709, ||r||/||r_0|| = 0.000119874
+LBFGS iteration 55 : ||r|| = 7.87381e-05, ||r||/||r_0|| = 5.37175e-05
+LBFGS iteration 56 : ||r|| = 7.30614e-05, ||r||/||r_0|| = 4.98447e-05
+LBFGS iteration 57 : ||r|| = 9.55919e-05, ||r||/||r_0|| = 6.52157e-05
+LBFGS iteration 58 : ||r|| = 0.000134287, ||r||/||r_0|| = 9.16148e-05
+LBFGS iteration 59 : ||r|| = 6.66417e-05, ||r||/||r_0|| = 4.5465e-05
+LBFGS iteration 60 : ||r|| = 5.38494e-05, ||r||/||r_0|| = 3.67377e-05
+LBFGS iteration 61 : ||r|| = 5.80937e-05, ||r||/||r_0|| = 3.96333e-05
+LBFGS iteration 62 : ||r|| = 8.22887e-05, ||r||/||r_0|| = 5.61399e-05
+LBFGS iteration 63 : ||r|| = 4.59653e-05, ||r||/||r_0|| = 3.1359e-05
+LBFGS iteration 64 : ||r|| = 4.21774e-05, ||r||/||r_0|| = 2.87747e-05
+LBFGS iteration 65 : ||r|| = 4.36417e-05, ||r||/||r_0|| = 2.97737e-05
+LBFGS iteration 66 : ||r|| = 0.000102056, ||r||/||r_0|| = 6.96257e-05
+LBFGS iteration 67 : ||r|| = 2.55212e-05, ||r||/||r_0|| = 1.74114e-05
+LBFGS iteration 68 : ||r|| = 1.74447e-05, ||r||/||r_0|| = 1.19013e-05
+LBFGS iteration 69 : ||r|| = 1.55053e-05, ||r||/||r_0|| = 1.05782e-05
+LBFGS iteration 70 : ||r|| = 2.81845e-05, ||r||/||r_0|| = 1.92283e-05
+LBFGS iteration 71 : ||r|| = 8.05057e-06, ||r||/||r_0|| = 5.49234e-06
+LBFGS iteration 72 : ||r|| = 3.16352e-06, ||r||/||r_0|| = 2.15825e-06
+LBFGS iteration 73 : ||r|| = 2.31988e-06, ||r||/||r_0|| = 1.58269e-06
+LBFGS iteration 74 : ||r|| = 2.24328e-06, ||r||/||r_0|| = 1.53043e-06
+LBFGS iteration 75 : ||r|| = 6.49278e-06, ||r||/||r_0|| = 4.42957e-06
+LBFGS iteration 76 : ||r|| = 1.24208e-06, ||r||/||r_0|| = 8.47383e-07
+LBFGS/Newton+GMRES converged in 76 iterations with a residual norm of 1.24208e-06.
+solver took 3.23983s.
+|| q_h - q_ex || / || q_ex || = 0.000247126
+|| t_h - t_ex || / || t_ex || = 0.0002417
@@ -0,0 +1,49 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00826646s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.055207s.
+Preconditioner took 4.3616e-05s.
+Newton iteration  0 : ||r|| = 1.46578
+Newton iteration  1 : ||r|| = 6.23817e-08, ||r||/||r_0|| = 4.25587e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 6.23817e-08.
+solver took 0.338429s.
+|| q_h - q_ex || / || q_ex || = 0.000247131
+|| t_h - t_ex || / || t_ex || = 0.000241709
@@ -0,0 +1,169 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0174704s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0193046s.
+Preconditioner took 6.1853e-05s.
+LBFGS iteration 0 : ||r|| = 1.60422
+LBFGS iteration 1 : ||r|| = 4.04305, ||r||/||r_0|| = 2.52026
+LBFGS iteration 2 : ||r|| = 2.27103, ||r||/||r_0|| = 1.41566
+LBFGS iteration 3 : ||r|| = 2.86497, ||r||/||r_0|| = 1.7859
+LBFGS iteration 4 : ||r|| = 8.10595, ||r||/||r_0|| = 5.0529
+LBFGS iteration 5 : ||r|| = 8.73464, ||r||/||r_0|| = 5.4448
+LBFGS iteration 6 : ||r|| = 1.87803, ||r||/||r_0|| = 1.17069
+LBFGS iteration 7 : ||r|| = 1.07044, ||r||/||r_0|| = 0.667268
+LBFGS iteration 8 : ||r|| = 1.19802, ||r||/||r_0|| = 0.746794
+LBFGS iteration 9 : ||r|| = 2.05643, ||r||/||r_0|| = 1.28189
+LBFGS iteration 10 : ||r|| = 1.71473, ||r||/||r_0|| = 1.06889
+LBFGS iteration 11 : ||r|| = 1.80177, ||r||/||r_0|| = 1.12315
+LBFGS iteration 12 : ||r|| = 2.94979, ||r||/||r_0|| = 1.83878
+LBFGS iteration 13 : ||r|| = 0.788424, ||r||/||r_0|| = 0.49147
+LBFGS iteration 14 : ||r|| = 0.688495, ||r||/||r_0|| = 0.429178
+LBFGS iteration 15 : ||r|| = 1.15113, ||r||/||r_0|| = 0.717567
+LBFGS iteration 16 : ||r|| = 1.20461, ||r||/||r_0|| = 0.750902
+LBFGS iteration 17 : ||r|| = 4.95942, ||r||/||r_0|| = 3.09149
+LBFGS iteration 18 : ||r|| = 0.596949, ||r||/||r_0|| = 0.372113
+LBFGS iteration 19 : ||r|| = 0.467761, ||r||/||r_0|| = 0.291582
+LBFGS iteration 20 : ||r|| = 0.71786, ||r||/||r_0|| = 0.447483
+LBFGS iteration 21 : ||r|| = 0.836852, ||r||/||r_0|| = 0.521658
+LBFGS iteration 22 : ||r|| = 2.59644, ||r||/||r_0|| = 1.61851
+LBFGS iteration 23 : ||r|| = 0.388821, ||r||/||r_0|| = 0.242374
+LBFGS iteration 24 : ||r|| = 0.234827, ||r||/||r_0|| = 0.146381
+LBFGS iteration 25 : ||r|| = 0.263661, ||r||/||r_0|| = 0.164355
+LBFGS iteration 26 : ||r|| = 0.277796, ||r||/||r_0|| = 0.173166
+LBFGS iteration 27 : ||r|| = 0.975136, ||r||/||r_0|| = 0.607858
+LBFGS iteration 28 : ||r|| = 0.128984, ||r||/||r_0|| = 0.0804028
+LBFGS iteration 29 : ||r|| = 0.0994523, ||r||/||r_0|| = 0.0619943
+LBFGS iteration 30 : ||r|| = 0.102656, ||r||/||r_0|| = 0.0639912
+LBFGS iteration 31 : ||r|| = 0.430616, ||r||/||r_0|| = 0.268427
+LBFGS iteration 32 : ||r|| = 0.107659, ||r||/||r_0|| = 0.06711
+LBFGS iteration 33 : ||r|| = 0.0659709, ||r||/||r_0|| = 0.0411234
+LBFGS iteration 34 : ||r|| = 0.108932, ||r||/||r_0|| = 0.0679038
+LBFGS iteration 35 : ||r|| = 0.10333, ||r||/||r_0|| = 0.0644116
+LBFGS iteration 36 : ||r|| = 0.393613, ||r||/||r_0|| = 0.245362
+LBFGS iteration 37 : ||r|| = 0.044456, ||r||/||r_0|| = 0.027712
+LBFGS iteration 38 : ||r|| = 0.0293365, ||r||/||r_0|| = 0.0182871
+LBFGS iteration 39 : ||r|| = 0.0325774, ||r||/||r_0|| = 0.0203074
+LBFGS iteration 40 : ||r|| = 0.0383684, ||r||/||r_0|| = 0.0239172
+LBFGS iteration 41 : ||r|| = 0.0935856, ||r||/||r_0|| = 0.0583372
+LBFGS iteration 42 : ||r|| = 0.0181591, ||r||/||r_0|| = 0.0113196
+LBFGS iteration 43 : ||r|| = 0.0101241, ||r||/||r_0|| = 0.0063109
+LBFGS iteration 44 : ||r|| = 0.0103064, ||r||/||r_0|| = 0.00642455
+LBFGS iteration 45 : ||r|| = 0.0136856, ||r||/||r_0|| = 0.00853103
+LBFGS iteration 46 : ||r|| = 0.0224226, ||r||/||r_0|| = 0.0139773
+LBFGS iteration 47 : ||r|| = 0.0121399, ||r||/||r_0|| = 0.00756747
+LBFGS iteration 48 : ||r|| = 0.00565715, ||r||/||r_0|| = 0.00352643
+LBFGS iteration 49 : ||r|| = 0.00519774, ||r||/||r_0|| = 0.00324005
+LBFGS iteration 50 : ||r|| = 0.00683834, ||r||/||r_0|| = 0.00426273
+LBFGS iteration 51 : ||r|| = 0.0102297, ||r||/||r_0|| = 0.00637677
+LBFGS iteration 52 : ||r|| = 0.0178293, ||r||/||r_0|| = 0.011114
+LBFGS iteration 53 : ||r|| = 0.00410073, ||r||/||r_0|| = 0.00255622
+LBFGS iteration 54 : ||r|| = 0.00214889, ||r||/||r_0|| = 0.00133952
+LBFGS iteration 55 : ||r|| = 0.00179143, ||r||/||r_0|| = 0.0011167
+LBFGS iteration 56 : ||r|| = 0.00228298, ||r||/||r_0|| = 0.00142311
+LBFGS iteration 57 : ||r|| = 0.00331611, ||r||/||r_0|| = 0.00206712
+LBFGS iteration 58 : ||r|| = 0.00287553, ||r||/||r_0|| = 0.00179248
+LBFGS iteration 59 : ||r|| = 0.00174206, ||r||/||r_0|| = 0.00108593
+LBFGS iteration 60 : ||r|| = 0.00197402, ||r||/||r_0|| = 0.00123052
+LBFGS iteration 61 : ||r|| = 0.00271139, ||r||/||r_0|| = 0.00169016
+LBFGS iteration 62 : ||r|| = 0.0033751, ||r||/||r_0|| = 0.00210389
+LBFGS iteration 63 : ||r|| = 0.00675991, ||r||/||r_0|| = 0.00421384
+LBFGS iteration 64 : ||r|| = 0.00199077, ||r||/||r_0|| = 0.00124096
+LBFGS iteration 65 : ||r|| = 0.00103921, ||r||/||r_0|| = 0.000647797
+LBFGS iteration 66 : ||r|| = 0.00130432, ||r||/||r_0|| = 0.000813055
+LBFGS iteration 67 : ||r|| = 0.00173231, ||r||/||r_0|| = 0.00107985
+LBFGS iteration 68 : ||r|| = 0.00255953, ||r||/||r_0|| = 0.0015955
+LBFGS iteration 69 : ||r|| = 0.00178072, ||r||/||r_0|| = 0.00111003
+LBFGS iteration 70 : ||r|| = 0.000654644, ||r||/||r_0|| = 0.000408077
+LBFGS iteration 71 : ||r|| = 0.000543947, ||r||/||r_0|| = 0.000339073
+LBFGS iteration 72 : ||r|| = 0.000693809, ||r||/||r_0|| = 0.000432491
+LBFGS iteration 73 : ||r|| = 0.00123584, ||r||/||r_0|| = 0.000770371
+LBFGS iteration 74 : ||r|| = 0.000501059, ||r||/||r_0|| = 0.000312339
+LBFGS iteration 75 : ||r|| = 0.000265266, ||r||/||r_0|| = 0.000165356
+LBFGS iteration 76 : ||r|| = 0.000251954, ||r||/||r_0|| = 0.000157057
+LBFGS iteration 77 : ||r|| = 0.000333886, ||r||/||r_0|| = 0.00020813
+LBFGS iteration 78 : ||r|| = 0.000522524, ||r||/||r_0|| = 0.000325719
+LBFGS iteration 79 : ||r|| = 0.000369836, ||r||/||r_0|| = 0.00023054
+LBFGS iteration 80 : ||r|| = 0.000157428, ||r||/||r_0|| = 9.81341e-05
+LBFGS iteration 81 : ||r|| = 0.000134986, ||r||/||r_0|| = 8.41443e-05
+LBFGS iteration 82 : ||r|| = 0.000153649, ||r||/||r_0|| = 9.57781e-05
+LBFGS iteration 83 : ||r|| = 0.000245621, ||r||/||r_0|| = 0.00015311
+LBFGS iteration 84 : ||r|| = 0.000197426, ||r||/||r_0|| = 0.000123067
+LBFGS iteration 85 : ||r|| = 6.29115e-05, ||r||/||r_0|| = 3.92164e-05
+LBFGS iteration 86 : ||r|| = 5.17471e-05, ||r||/||r_0|| = 3.22569e-05
+LBFGS iteration 87 : ||r|| = 6.68762e-05, ||r||/||r_0|| = 4.16877e-05
+LBFGS iteration 88 : ||r|| = 7.26244e-05, ||r||/||r_0|| = 4.52709e-05
+LBFGS iteration 89 : ||r|| = 0.000227688, ||r||/||r_0|| = 0.000141931
+LBFGS iteration 90 : ||r|| = 3.31977e-05, ||r||/||r_0|| = 2.0694e-05
+LBFGS iteration 91 : ||r|| = 2.65641e-05, ||r||/||r_0|| = 1.65589e-05
+LBFGS iteration 92 : ||r|| = 3.49512e-05, ||r||/||r_0|| = 2.17871e-05
+LBFGS iteration 93 : ||r|| = 4.97308e-05, ||r||/||r_0|| = 3.10001e-05
+LBFGS iteration 94 : ||r|| = 3.34232e-05, ||r||/||r_0|| = 2.08346e-05
+LBFGS iteration 95 : ||r|| = 1.1803e-05, ||r||/||r_0|| = 7.35749e-06
+LBFGS iteration 96 : ||r|| = 1.02902e-05, ||r||/||r_0|| = 6.41446e-06
+LBFGS iteration 97 : ||r|| = 1.30043e-05, ||r||/||r_0|| = 8.10633e-06
+LBFGS iteration 98 : ||r|| = 2.26578e-05, ||r||/||r_0|| = 1.41239e-05
+LBFGS iteration 99 : ||r|| = 2.0364e-05, ||r||/||r_0|| = 1.2694e-05
+LBFGS iteration 100 : ||r|| = 1.01336e-05, ||r||/||r_0|| = 6.31686e-06
+LBFGS iteration 101 : ||r|| = 9.57449e-06, ||r||/||r_0|| = 5.96833e-06
+LBFGS iteration 102 : ||r|| = 1.17016e-05, ||r||/||r_0|| = 7.29425e-06
+LBFGS iteration 103 : ||r|| = 2.72813e-05, ||r||/||r_0|| = 1.7006e-05
+LBFGS iteration 104 : ||r|| = 9.72679e-06, ||r||/||r_0|| = 6.06327e-06
+LBFGS iteration 105 : ||r|| = 6.59627e-06, ||r||/||r_0|| = 4.11183e-06
+LBFGS iteration 106 : ||r|| = 7.66233e-06, ||r||/||r_0|| = 4.77637e-06
+LBFGS iteration 107 : ||r|| = 1.1227e-05, ||r||/||r_0|| = 6.99842e-06
+LBFGS iteration 108 : ||r|| = 7.81538e-06, ||r||/||r_0|| = 4.87177e-06
+LBFGS iteration 109 : ||r|| = 6.73626e-06, ||r||/||r_0|| = 4.1991e-06
+LBFGS iteration 110 : ||r|| = 5.02859e-06, ||r||/||r_0|| = 3.1346e-06
+LBFGS iteration 111 : ||r|| = 4.63857e-06, ||r||/||r_0|| = 2.89149e-06
+LBFGS iteration 112 : ||r|| = 7.50298e-06, ||r||/||r_0|| = 4.67704e-06
+LBFGS iteration 113 : ||r|| = 5.96133e-06, ||r||/||r_0|| = 3.71604e-06
+LBFGS iteration 114 : ||r|| = 3.93594e-06, ||r||/||r_0|| = 2.45349e-06
+LBFGS iteration 115 : ||r|| = 3.71031e-06, ||r||/||r_0|| = 2.31285e-06
+LBFGS iteration 116 : ||r|| = 4.97969e-06, ||r||/||r_0|| = 3.10413e-06
+LBFGS iteration 117 : ||r|| = 8.19517e-06, ||r||/||r_0|| = 5.10852e-06
+LBFGS iteration 118 : ||r|| = 2.17669e-06, ||r||/||r_0|| = 1.35685e-06
+LBFGS iteration 119 : ||r|| = 1.66053e-06, ||r||/||r_0|| = 1.0351e-06
+LBFGS iteration 120 : ||r|| = 1.84e-06, ||r||/||r_0|| = 1.14698e-06
+LBFGS iteration 121 : ||r|| = 3.54175e-06, ||r||/||r_0|| = 2.20777e-06
+LBFGS iteration 122 : ||r|| = 1.39257e-06, ||r||/||r_0|| = 8.6807e-07
+LBFGS/Newton+GMRES converged in 122 iterations with a residual norm of 1.39257e-06.
+solver took 21.8909s.
+|| q_h - q_ex || / || q_ex || = 6.12087e-06
+|| t_h - t_ex || / || t_ex || = 3.90288e-06
@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0137397s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0117625s.
+Preconditioner took 3.3236e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.98725e-08, ||r||/||r_0|| = 3.10884e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.98725e-08.
+solver took 0.601921s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06
@@ -0,0 +1,170 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.0109196s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.021188s.
+Preconditioner took 5.675e-05s.
+LBFGS iteration 0 : ||r|| = 1.60422
+LBFGS iteration 1 : ||r|| = 4.04305, ||r||/||r_0|| = 2.52026
+LBFGS iteration 2 : ||r|| = 2.27103, ||r||/||r_0|| = 1.41566
+LBFGS iteration 3 : ||r|| = 2.86497, ||r||/||r_0|| = 1.7859
+LBFGS iteration 4 : ||r|| = 8.10595, ||r||/||r_0|| = 5.0529
+LBFGS iteration 5 : ||r|| = 8.73464, ||r||/||r_0|| = 5.4448
+LBFGS iteration 6 : ||r|| = 1.87803, ||r||/||r_0|| = 1.17069
+LBFGS iteration 7 : ||r|| = 1.07044, ||r||/||r_0|| = 0.667268
+LBFGS iteration 8 : ||r|| = 1.19802, ||r||/||r_0|| = 0.746794
+LBFGS iteration 9 : ||r|| = 2.05643, ||r||/||r_0|| = 1.28189
+LBFGS iteration 10 : ||r|| = 1.71473, ||r||/||r_0|| = 1.06889
+LBFGS iteration 11 : ||r|| = 1.80177, ||r||/||r_0|| = 1.12315
+LBFGS iteration 12 : ||r|| = 2.94979, ||r||/||r_0|| = 1.83878
+LBFGS iteration 13 : ||r|| = 0.788424, ||r||/||r_0|| = 0.49147
+LBFGS iteration 14 : ||r|| = 0.688495, ||r||/||r_0|| = 0.429178
+LBFGS iteration 15 : ||r|| = 1.15113, ||r||/||r_0|| = 0.717567
+LBFGS iteration 16 : ||r|| = 1.20461, ||r||/||r_0|| = 0.750902
+LBFGS iteration 17 : ||r|| = 4.95942, ||r||/||r_0|| = 3.09149
+LBFGS iteration 18 : ||r|| = 0.596949, ||r||/||r_0|| = 0.372113
+LBFGS iteration 19 : ||r|| = 0.467761, ||r||/||r_0|| = 0.291582
+LBFGS iteration 20 : ||r|| = 0.71786, ||r||/||r_0|| = 0.447483
+LBFGS iteration 21 : ||r|| = 0.836852, ||r||/||r_0|| = 0.521658
+LBFGS iteration 22 : ||r|| = 2.59644, ||r||/||r_0|| = 1.61851
+LBFGS iteration 23 : ||r|| = 0.388821, ||r||/||r_0|| = 0.242374
+LBFGS iteration 24 : ||r|| = 0.234827, ||r||/||r_0|| = 0.146381
+LBFGS iteration 25 : ||r|| = 0.263661, ||r||/||r_0|| = 0.164355
+LBFGS iteration 26 : ||r|| = 0.277796, ||r||/||r_0|| = 0.173166
+LBFGS iteration 27 : ||r|| = 0.975136, ||r||/||r_0|| = 0.607858
+LBFGS iteration 28 : ||r|| = 0.128984, ||r||/||r_0|| = 0.0804028
+LBFGS iteration 29 : ||r|| = 0.0994523, ||r||/||r_0|| = 0.0619943
+LBFGS iteration 30 : ||r|| = 0.102656, ||r||/||r_0|| = 0.0639912
+LBFGS iteration 31 : ||r|| = 0.430616, ||r||/||r_0|| = 0.268427
+LBFGS iteration 32 : ||r|| = 0.107659, ||r||/||r_0|| = 0.06711
+LBFGS iteration 33 : ||r|| = 0.0659709, ||r||/||r_0|| = 0.0411234
+LBFGS iteration 34 : ||r|| = 0.108932, ||r||/||r_0|| = 0.0679038
+LBFGS iteration 35 : ||r|| = 0.10333, ||r||/||r_0|| = 0.0644116
+LBFGS iteration 36 : ||r|| = 0.393613, ||r||/||r_0|| = 0.245362
+LBFGS iteration 37 : ||r|| = 0.044456, ||r||/||r_0|| = 0.027712
+LBFGS iteration 38 : ||r|| = 0.0293365, ||r||/||r_0|| = 0.0182871
+LBFGS iteration 39 : ||r|| = 0.0325774, ||r||/||r_0|| = 0.0203074
+LBFGS iteration 40 : ||r|| = 0.0383684, ||r||/||r_0|| = 0.0239172
+LBFGS iteration 41 : ||r|| = 0.0935856, ||r||/||r_0|| = 0.0583372
+LBFGS iteration 42 : ||r|| = 0.0181591, ||r||/||r_0|| = 0.0113196
+LBFGS iteration 43 : ||r|| = 0.0101241, ||r||/||r_0|| = 0.0063109
+LBFGS iteration 44 : ||r|| = 0.0103064, ||r||/||r_0|| = 0.00642455
+LBFGS iteration 45 : ||r|| = 0.0136856, ||r||/||r_0|| = 0.00853103
+LBFGS iteration 46 : ||r|| = 0.0224226, ||r||/||r_0|| = 0.0139773
+LBFGS iteration 47 : ||r|| = 0.0121399, ||r||/||r_0|| = 0.00756747
+LBFGS iteration 48 : ||r|| = 0.00565715, ||r||/||r_0|| = 0.00352643
+LBFGS iteration 49 : ||r|| = 0.00519774, ||r||/||r_0|| = 0.00324005
+LBFGS iteration 50 : ||r|| = 0.00683834, ||r||/||r_0|| = 0.00426273
+LBFGS iteration 51 : ||r|| = 0.0102297, ||r||/||r_0|| = 0.00637677
+LBFGS iteration 52 : ||r|| = 0.0178293, ||r||/||r_0|| = 0.011114
+LBFGS iteration 53 : ||r|| = 0.00410073, ||r||/||r_0|| = 0.00255622
+LBFGS iteration 54 : ||r|| = 0.00214889, ||r||/||r_0|| = 0.00133952
+LBFGS iteration 55 : ||r|| = 0.00179143, ||r||/||r_0|| = 0.0011167
+LBFGS iteration 56 : ||r|| = 0.00228298, ||r||/||r_0|| = 0.00142311
+LBFGS iteration 57 : ||r|| = 0.00331611, ||r||/||r_0|| = 0.00206712
+LBFGS iteration 58 : ||r|| = 0.00287553, ||r||/||r_0|| = 0.00179248
+LBFGS iteration 59 : ||r|| = 0.00174206, ||r||/||r_0|| = 0.00108593
+LBFGS iteration 60 : ||r|| = 0.00197402, ||r||/||r_0|| = 0.00123052
+LBFGS iteration 61 : ||r|| = 0.00271139, ||r||/||r_0|| = 0.00169016
+LBFGS iteration 62 : ||r|| = 0.0033751, ||r||/||r_0|| = 0.00210389
+LBFGS iteration 63 : ||r|| = 0.00675992, ||r||/||r_0|| = 0.00421385
+LBFGS iteration 64 : ||r|| = 0.00199077, ||r||/||r_0|| = 0.00124096
+LBFGS iteration 65 : ||r|| = 0.00103921, ||r||/||r_0|| = 0.000647797
+LBFGS iteration 66 : ||r|| = 0.00130432, ||r||/||r_0|| = 0.000813055
+LBFGS iteration 67 : ||r|| = 0.00173231, ||r||/||r_0|| = 0.00107985
+LBFGS iteration 68 : ||r|| = 0.00255953, ||r||/||r_0|| = 0.0015955
+LBFGS iteration 69 : ||r|| = 0.00178073, ||r||/||r_0|| = 0.00111003
+LBFGS iteration 70 : ||r|| = 0.000654644, ||r||/||r_0|| = 0.000408077
+LBFGS iteration 71 : ||r|| = 0.000543947, ||r||/||r_0|| = 0.000339073
+LBFGS iteration 72 : ||r|| = 0.000693809, ||r||/||r_0|| = 0.000432491
+LBFGS iteration 73 : ||r|| = 0.00123584, ||r||/||r_0|| = 0.000770371
+LBFGS iteration 74 : ||r|| = 0.000501059, ||r||/||r_0|| = 0.000312339
+LBFGS iteration 75 : ||r|| = 0.000265266, ||r||/||r_0|| = 0.000165356
+LBFGS iteration 76 : ||r|| = 0.000251953, ||r||/||r_0|| = 0.000157057
+LBFGS iteration 77 : ||r|| = 0.000333886, ||r||/||r_0|| = 0.00020813
+LBFGS iteration 78 : ||r|| = 0.000522523, ||r||/||r_0|| = 0.000325719
+LBFGS iteration 79 : ||r|| = 0.000369834, ||r||/||r_0|| = 0.000230539
+LBFGS iteration 80 : ||r|| = 0.000157428, ||r||/||r_0|| = 9.81338e-05
+LBFGS iteration 81 : ||r|| = 0.000134985, ||r||/||r_0|| = 8.41439e-05
+LBFGS iteration 82 : ||r|| = 0.000153647, ||r||/||r_0|| = 9.5777e-05
+LBFGS iteration 83 : ||r|| = 0.000245494, ||r||/||r_0|| = 0.00015303
+LBFGS iteration 84 : ||r|| = 0.000197097, ||r||/||r_0|| = 0.000122862
+LBFGS iteration 85 : ||r|| = 6.28938e-05, ||r||/||r_0|| = 3.92053e-05
+LBFGS iteration 86 : ||r|| = 5.17492e-05, ||r||/||r_0|| = 3.22582e-05
+LBFGS iteration 87 : ||r|| = 6.68573e-05, ||r||/||r_0|| = 4.1676e-05
+LBFGS iteration 88 : ||r|| = 7.20488e-05, ||r||/||r_0|| = 4.49121e-05
+LBFGS iteration 89 : ||r|| = 0.000230595, ||r||/||r_0|| = 0.000143743
+LBFGS iteration 90 : ||r|| = 3.32498e-05, ||r||/||r_0|| = 2.07265e-05
+LBFGS iteration 91 : ||r|| = 2.65435e-05, ||r||/||r_0|| = 1.65461e-05
+LBFGS iteration 92 : ||r|| = 3.48386e-05, ||r||/||r_0|| = 2.17169e-05
+LBFGS iteration 93 : ||r|| = 4.93021e-05, ||r||/||r_0|| = 3.07328e-05
+LBFGS iteration 94 : ||r|| = 3.37321e-05, ||r||/||r_0|| = 2.10271e-05
+LBFGS iteration 95 : ||r|| = 1.17848e-05, ||r||/||r_0|| = 7.34615e-06
+LBFGS iteration 96 : ||r|| = 1.02097e-05, ||r||/||r_0|| = 6.3643e-06
+LBFGS iteration 97 : ||r|| = 1.29555e-05, ||r||/||r_0|| = 8.0759e-06
+LBFGS iteration 98 : ||r|| = 2.22505e-05, ||r||/||r_0|| = 1.387e-05
+LBFGS iteration 99 : ||r|| = 2.10878e-05, ||r||/||r_0|| = 1.31452e-05
+LBFGS iteration 100 : ||r|| = 1.02078e-05, ||r||/||r_0|| = 6.36309e-06
+LBFGS iteration 101 : ||r|| = 9.50017e-06, ||r||/||r_0|| = 5.922e-06
+LBFGS iteration 102 : ||r|| = 1.15863e-05, ||r||/||r_0|| = 7.22239e-06
+LBFGS iteration 103 : ||r|| = 2.69417e-05, ||r||/||r_0|| = 1.67943e-05
+LBFGS iteration 104 : ||r|| = 9.94455e-06, ||r||/||r_0|| = 6.19901e-06
+LBFGS iteration 105 : ||r|| = 6.55722e-06, ||r||/||r_0|| = 4.08749e-06
+LBFGS iteration 106 : ||r|| = 7.61877e-06, ||r||/||r_0|| = 4.74921e-06
+LBFGS iteration 107 : ||r|| = 1.09382e-05, ||r||/||r_0|| = 6.81844e-06
+LBFGS iteration 108 : ||r|| = 7.76942e-06, ||r||/||r_0|| = 4.84313e-06
+LBFGS iteration 109 : ||r|| = 7.29928e-06, ||r||/||r_0|| = 4.55006e-06
+LBFGS iteration 110 : ||r|| = 4.93978e-06, ||r||/||r_0|| = 3.07925e-06
+LBFGS iteration 111 : ||r|| = 4.5857e-06, ||r||/||r_0|| = 2.85853e-06
+LBFGS iteration 112 : ||r|| = 7.23401e-06, ||r||/||r_0|| = 4.50937e-06
+LBFGS iteration 113 : ||r|| = 6.2086e-06, ||r||/||r_0|| = 3.87018e-06
+LBFGS iteration 114 : ||r|| = 3.91586e-06, ||r||/||r_0|| = 2.44098e-06
+LBFGS iteration 115 : ||r|| = 3.8682e-06, ||r||/||r_0|| = 2.41127e-06
+LBFGS iteration 116 : ||r|| = 4.77772e-06, ||r||/||r_0|| = 2.97823e-06
+LBFGS iteration 117 : ||r|| = 1.05549e-05, ||r||/||r_0|| = 6.57945e-06
+LBFGS iteration 118 : ||r|| = 2.32515e-06, ||r||/||r_0|| = 1.4494e-06
+LBFGS iteration 119 : ||r|| = 1.65531e-06, ||r||/||r_0|| = 1.03185e-06
+LBFGS iteration 120 : ||r|| = 1.83133e-06, ||r||/||r_0|| = 1.14157e-06
+LBFGS iteration 121 : ||r|| = 2.81453e-06, ||r||/||r_0|| = 1.75445e-06
+LBFGS iteration 122 : ||r|| = 1.83419e-06, ||r||/||r_0|| = 1.14336e-06
+LBFGS iteration 123 : ||r|| = 8.4473e-07, ||r||/||r_0|| = 5.26568e-07
+LBFGS/Newton+GMRES converged in 123 iterations with a residual norm of 8.4473e-07.
+solver took 9.23797s.
+|| q_h - q_ex || / || q_ex || = 6.11146e-06
+|| t_h - t_ex || / || t_ex || = 3.90229e-06
@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00863252s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0111083s.
+Preconditioner took 1.9831e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.77667e-08, ||r||/||r_0|| = 2.97757e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.77667e-08.
+solver took 0.454486s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06
@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00990361s.
+***********************************************************
+dim(V) = 1860
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3420
+***********************************************************
+Assembly took 0.0162211s.
+Preconditioner took 2.4778e-05s.
+Newton iteration  0 : ||r|| = 1.60422
+Newton iteration  1 : ||r|| = 4.77667e-08, ||r||/||r_0|| = 2.97757e-08
+Newton+GMRES+GS/Newton+GMRES converged in 1 iterations with a residual norm of 4.77667e-08.
+solver took 0.461365s.
+|| q_h - q_ex || / || q_ex || = 6.10477e-06
+|| t_h - t_ex || / || t_ex || = 3.90155e-06
@@ -0,0 +1,231 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0122702s.
+Preconditioner took 0.00343498s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.828288
+   Pass :  1   Iteration :   1  ||B r|| = 0.828288
+   Pass :  1   Iteration :   2  ||B r|| = 0.780392
+   Pass :  1   Iteration :   3  ||B r|| = 0.775902
+   Pass :  1   Iteration :   4  ||B r|| = 0.718999
+   Pass :  1   Iteration :   5  ||B r|| = 0.712741
+   Pass :  1   Iteration :   6  ||B r|| = 0.709216
+   Pass :  1   Iteration :   7  ||B r|| = 0.699357
+   Pass :  1   Iteration :   8  ||B r|| = 0.685558
+   Pass :  1   Iteration :   9  ||B r|| = 0.624758
+   Pass :  1   Iteration :  10  ||B r|| = 0.61651
+   Pass :  1   Iteration :  11  ||B r|| = 0.491672
+   Pass :  1   Iteration :  12  ||B r|| = 0.490509
+   Pass :  1   Iteration :  13  ||B r|| = 0.43273
+   Pass :  1   Iteration :  14  ||B r|| = 0.432532
+   Pass :  1   Iteration :  15  ||B r|| = 0.391607
+   Pass :  1   Iteration :  16  ||B r|| = 0.387505
+   Pass :  1   Iteration :  17  ||B r|| = 0.369287
+   Pass :  1   Iteration :  18  ||B r|| = 0.349727
+   Pass :  1   Iteration :  19  ||B r|| = 0.344534
+   Pass :  1   Iteration :  20  ||B r|| = 0.308102
+   Pass :  1   Iteration :  21  ||B r|| = 0.307918
+   Pass :  1   Iteration :  22  ||B r|| = 0.275424
+   Pass :  1   Iteration :  23  ||B r|| = 0.275336
+   Pass :  1   Iteration :  24  ||B r|| = 0.241166
+   Pass :  1   Iteration :  25  ||B r|| = 0.236098
+   Pass :  1   Iteration :  26  ||B r|| = 0.220482
+   Pass :  1   Iteration :  27  ||B r|| = 0.209195
+   Pass :  1   Iteration :  28  ||B r|| = 0.203284
+   Pass :  1   Iteration :  29  ||B r|| = 0.184134
+   Pass :  1   Iteration :  30  ||B r|| = 0.183885
+   Pass :  1   Iteration :  31  ||B r|| = 0.158572
+   Pass :  1   Iteration :  32  ||B r|| = 0.15785
+   Pass :  1   Iteration :  33  ||B r|| = 0.128252
+   Pass :  1   Iteration :  34  ||B r|| = 0.121277
+   Pass :  1   Iteration :  35  ||B r|| = 0.105019
+   Pass :  1   Iteration :  36  ||B r|| = 0.0877653
+   Pass :  1   Iteration :  37  ||B r|| = 0.0857034
+   Pass :  1   Iteration :  38  ||B r|| = 0.0695776
+   Pass :  1   Iteration :  39  ||B r|| = 0.0693421
+   Pass :  1   Iteration :  40  ||B r|| = 0.060764
+   Pass :  1   Iteration :  41  ||B r|| = 0.0583294
+   Pass :  1   Iteration :  42  ||B r|| = 0.0513009
+   Pass :  1   Iteration :  43  ||B r|| = 0.046381
+   Pass :  1   Iteration :  44  ||B r|| = 0.0446401
+   Pass :  1   Iteration :  45  ||B r|| = 0.0351366
+   Pass :  1   Iteration :  46  ||B r|| = 0.0350703
+   Pass :  1   Iteration :  47  ||B r|| = 0.0285254
+   Pass :  1   Iteration :  48  ||B r|| = 0.0275435
+   Pass :  1   Iteration :  49  ||B r|| = 0.0233101
+   Pass :  1   Iteration :  50  ||B r|| = 0.0205522
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.0201743
+   Pass :  2   Iteration :  52  ||B r|| = 0.0178036
+   Pass :  2   Iteration :  53  ||B r|| = 0.0177657
+   Pass :  2   Iteration :  54  ||B r|| = 0.0155379
+   Pass :  2   Iteration :  55  ||B r|| = 0.0145024
+   Pass :  2   Iteration :  56  ||B r|| = 0.0129692
+   Pass :  2   Iteration :  57  ||B r|| = 0.0111895
+   Pass :  2   Iteration :  58  ||B r|| = 0.0106264
+   Pass :  2   Iteration :  59  ||B r|| = 0.00883739
+   Pass :  2   Iteration :  60  ||B r|| = 0.00881869
+   Pass :  2   Iteration :  61  ||B r|| = 0.00734547
+   Pass :  2   Iteration :  62  ||B r|| = 0.00727023
+   Pass :  2   Iteration :  63  ||B r|| = 0.00664677
+   Pass :  2   Iteration :  64  ||B r|| = 0.00606592
+   Pass :  2   Iteration :  65  ||B r|| = 0.00584805
+   Pass :  2   Iteration :  66  ||B r|| = 0.00471596
+   Pass :  2   Iteration :  67  ||B r|| = 0.00467814
+   Pass :  2   Iteration :  68  ||B r|| = 0.00343373
+   Pass :  2   Iteration :  69  ||B r|| = 0.0034201
+   Pass :  2   Iteration :  70  ||B r|| = 0.00280534
+   Pass :  2   Iteration :  71  ||B r|| = 0.00270379
+   Pass :  2   Iteration :  72  ||B r|| = 0.0025783
+   Pass :  2   Iteration :  73  ||B r|| = 0.0022472
+   Pass :  2   Iteration :  74  ||B r|| = 0.00221863
+   Pass :  2   Iteration :  75  ||B r|| = 0.00186269
+   Pass :  2   Iteration :  76  ||B r|| = 0.00186179
+   Pass :  2   Iteration :  77  ||B r|| = 0.00160985
+   Pass :  2   Iteration :  78  ||B r|| = 0.00160018
+   Pass :  2   Iteration :  79  ||B r|| = 0.00148445
+   Pass :  2   Iteration :  80  ||B r|| = 0.00141886
+   Pass :  2   Iteration :  81  ||B r|| = 0.00139003
+   Pass :  2   Iteration :  82  ||B r|| = 0.00125305
+   Pass :  2   Iteration :  83  ||B r|| = 0.00124651
+   Pass :  2   Iteration :  84  ||B r|| = 0.00111105
+   Pass :  2   Iteration :  85  ||B r|| = 0.00110481
+   Pass :  2   Iteration :  86  ||B r|| = 0.001019
+   Pass :  2   Iteration :  87  ||B r|| = 0.000986979
+   Pass :  2   Iteration :  88  ||B r|| = 0.000943191
+   Pass :  2   Iteration :  89  ||B r|| = 0.000887917
+   Pass :  2   Iteration :  90  ||B r|| = 0.000878207
+   Pass :  2   Iteration :  91  ||B r|| = 0.000792828
+   Pass :  2   Iteration :  92  ||B r|| = 0.000792314
+   Pass :  2   Iteration :  93  ||B r|| = 0.00067918
+   Pass :  2   Iteration :  94  ||B r|| = 0.000661497
+   Pass :  2   Iteration :  95  ||B r|| = 0.000607798
+   Pass :  2   Iteration :  96  ||B r|| = 0.000585659
+   Pass :  2   Iteration :  97  ||B r|| = 0.000575458
+   Pass :  2   Iteration :  98  ||B r|| = 0.000536371
+   Pass :  2   Iteration :  99  ||B r|| = 0.000533329
+   Pass :  2   Iteration : 100  ||B r|| = 0.000476474
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.000476389
+   Pass :  3   Iteration : 102  ||B r|| = 0.000450568
+   Pass :  3   Iteration : 103  ||B r|| = 0.00044946
+   Pass :  3   Iteration : 104  ||B r|| = 0.000448032
+   Pass :  3   Iteration : 105  ||B r|| = 0.000436727
+   Pass :  3   Iteration : 106  ||B r|| = 0.000433054
+   Pass :  3   Iteration : 107  ||B r|| = 0.000384572
+   Pass :  3   Iteration : 108  ||B r|| = 0.000384151
+   Pass :  3   Iteration : 109  ||B r|| = 0.000326889
+   Pass :  3   Iteration : 110  ||B r|| = 0.000320214
+   Pass :  3   Iteration : 111  ||B r|| = 0.000295531
+   Pass :  3   Iteration : 112  ||B r|| = 0.00028017
+   Pass :  3   Iteration : 113  ||B r|| = 0.000271805
+   Pass :  3   Iteration : 114  ||B r|| = 0.000253182
+   Pass :  3   Iteration : 115  ||B r|| = 0.000251705
+   Pass :  3   Iteration : 116  ||B r|| = 0.000224202
+   Pass :  3   Iteration : 117  ||B r|| = 0.00022401
+   Pass :  3   Iteration : 118  ||B r|| = 0.000201373
+   Pass :  3   Iteration : 119  ||B r|| = 0.000195487
+   Pass :  3   Iteration : 120  ||B r|| = 0.000178312
+   Pass :  3   Iteration : 121  ||B r|| = 0.000163707
+   Pass :  3   Iteration : 122  ||B r|| = 0.000159212
+   Pass :  3   Iteration : 123  ||B r|| = 0.000143717
+   Pass :  3   Iteration : 124  ||B r|| = 0.000142938
+   Pass :  3   Iteration : 125  ||B r|| = 0.000129618
+   Pass :  3   Iteration : 126  ||B r|| = 0.000128535
+   Pass :  3   Iteration : 127  ||B r|| = 0.000120081
+   Pass :  3   Iteration : 128  ||B r|| = 0.000114142
+   Pass :  3   Iteration : 129  ||B r|| = 0.000109227
+   Pass :  3   Iteration : 130  ||B r|| = 9.74187e-05
+   Pass :  3   Iteration : 131  ||B r|| = 9.41802e-05
+   Pass :  3   Iteration : 132  ||B r|| = 7.97569e-05
+   Pass :  3   Iteration : 133  ||B r|| = 7.97329e-05
+   Pass :  3   Iteration : 134  ||B r|| = 6.96569e-05
+   Pass :  3   Iteration : 135  ||B r|| = 6.80129e-05
+   Pass :  3   Iteration : 136  ||B r|| = 6.39905e-05
+   Pass :  3   Iteration : 137  ||B r|| = 5.48303e-05
+   Pass :  3   Iteration : 138  ||B r|| = 5.33803e-05
+   Pass :  3   Iteration : 139  ||B r|| = 4.51005e-05
+   Pass :  3   Iteration : 140  ||B r|| = 4.47538e-05
+   Pass :  3   Iteration : 141  ||B r|| = 3.79739e-05
+   Pass :  3   Iteration : 142  ||B r|| = 3.79237e-05
+   Pass :  3   Iteration : 143  ||B r|| = 3.34755e-05
+   Pass :  3   Iteration : 144  ||B r|| = 3.19968e-05
+   Pass :  3   Iteration : 145  ||B r|| = 3.00248e-05
+   Pass :  3   Iteration : 146  ||B r|| = 2.43567e-05
+   Pass :  3   Iteration : 147  ||B r|| = 2.40027e-05
+   Pass :  3   Iteration : 148  ||B r|| = 1.75885e-05
+   Pass :  3   Iteration : 149  ||B r|| = 1.74341e-05
+   Pass :  3   Iteration : 150  ||B r|| = 1.38964e-05
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 1.33084e-05
+   Pass :  4   Iteration : 152  ||B r|| = 1.25291e-05
+   Pass :  4   Iteration : 153  ||B r|| = 1.15613e-05
+   Pass :  4   Iteration : 154  ||B r|| = 1.15039e-05
+   Pass :  4   Iteration : 155  ||B r|| = 8.97445e-06
+   Pass :  4   Iteration : 156  ||B r|| = 8.93619e-06
+   Pass :  4   Iteration : 157  ||B r|| = 7.17725e-06
+   Pass :  4   Iteration : 158  ||B r|| = 7.03949e-06
+   Pass :  4   Iteration : 159  ||B r|| = 6.28998e-06
+   Pass :  4   Iteration : 160  ||B r|| = 5.80418e-06
+   Pass :  4   Iteration : 161  ||B r|| = 5.6565e-06
+   Pass :  4   Iteration : 162  ||B r|| = 4.98291e-06
+   Pass :  4   Iteration : 163  ||B r|| = 4.97198e-06
+   Pass :  4   Iteration : 164  ||B r|| = 4.1327e-06
+   Pass :  4   Iteration : 165  ||B r|| = 4.04729e-06
+   Pass :  4   Iteration : 166  ||B r|| = 3.41458e-06
+   Pass :  4   Iteration : 167  ||B r|| = 3.2682e-06
+   Pass :  4   Iteration : 168  ||B r|| = 3.07084e-06
+   Pass :  4   Iteration : 169  ||B r|| = 2.6426e-06
+   Pass :  4   Iteration : 170  ||B r|| = 2.63354e-06
+   Pass :  4   Iteration : 171  ||B r|| = 2.17891e-06
+   Pass :  4   Iteration : 172  ||B r|| = 2.15133e-06
+   Pass :  4   Iteration : 173  ||B r|| = 1.91418e-06
+   Pass :  4   Iteration : 174  ||B r|| = 1.87277e-06
+   Pass :  4   Iteration : 175  ||B r|| = 1.75707e-06
+   Pass :  4   Iteration : 176  ||B r|| = 1.66039e-06
+   Pass :  4   Iteration : 177  ||B r|| = 1.62259e-06
+   Pass :  4   Iteration : 178  ||B r|| = 1.51352e-06
+   Pass :  4   Iteration : 179  ||B r|| = 1.51341e-06
+   Pass :  4   Iteration : 180  ||B r|| = 1.35973e-06
+   Pass :  4   Iteration : 181  ||B r|| = 1.34071e-06
+   Pass :  4   Iteration : 182  ||B r|| = 1.2227e-06
+   Pass :  4   Iteration : 183  ||B r|| = 1.16459e-06
+   Pass :  4   Iteration : 184  ||B r|| = 1.10473e-06
+   Pass :  4   Iteration : 185  ||B r|| = 9.95649e-07
+   Pass :  4   Iteration : 186  ||B r|| = 9.93491e-07
+   Pass :  4   Iteration : 187  ||B r|| = 9.20855e-07
+   Pass :  4   Iteration : 188  ||B r|| = 9.17534e-07
+   Pass :  4   Iteration : 189  ||B r|| = 8.48816e-07
+   Pass :  4   Iteration : 190  ||B r|| = 8.13729e-07
+GMRES+GS converged in 190 iterations with a residual norm of 8.13729e-07.
+GMRES solver took 0.110362s.
+|| q_h - q_ex || / || q_ex || = 1.02359e-06
+|| t_h - t_ex || / || t_ex || = 1.03461e-06
@@ -0,0 +1,420 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.0167388s.
+Preconditioner took 0.00560065s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+GMRES solver took 0.203855s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05
@@ -0,0 +1,60 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.0120309s.
+Preconditioner took 9.286e-06s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.96731
+   Pass :  1   Iteration :   1  ||B r|| = 1.24082
+   Pass :  1   Iteration :   2  ||B r|| = 0.785152
+   Pass :  1   Iteration :   3  ||B r|| = 0.612962
+   Pass :  1   Iteration :   4  ||B r|| = 0.444865
+   Pass :  1   Iteration :   5  ||B r|| = 0.308536
+   Pass :  1   Iteration :   6  ||B r|| = 0.181062
+   Pass :  1   Iteration :   7  ||B r|| = 0.0872824
+   Pass :  1   Iteration :   8  ||B r|| = 0.048816
+   Pass :  1   Iteration :   9  ||B r|| = 0.0234022
+   Pass :  1   Iteration :  10  ||B r|| = 0.0119249
+   Pass :  1   Iteration :  11  ||B r|| = 0.00419618
+   Pass :  1   Iteration :  12  ||B r|| = 0.00219869
+   Pass :  1   Iteration :  13  ||B r|| = 0.00115642
+   Pass :  1   Iteration :  14  ||B r|| = 0.000637756
+   Pass :  1   Iteration :  15  ||B r|| = 0.000297414
+   Pass :  1   Iteration :  16  ||B r|| = 0.000196751
+   Pass :  1   Iteration :  17  ||B r|| = 0.000123272
+   Pass :  1   Iteration :  18  ||B r|| = 6.14247e-05
+   Pass :  1   Iteration :  19  ||B r|| = 2.32696e-05
+   Pass :  1   Iteration :  20  ||B r|| = 1.13978e-05
+   Pass :  1   Iteration :  21  ||B r|| = 4.39964e-06
+   Pass :  1   Iteration :  22  ||B r|| = 1.71455e-06
+GMRES+GS converged in 22 iterations with a residual norm of 1.71455e-06.
+GMRES solver took 0.00161297s.
+|| q_h - q_ex || / || q_ex || = 1.03793e-05
+|| t_h - t_ex || / || t_ex || = 1.12283e-05
@@ -0,0 +1,424 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.113936s.
+Preconditioner took 0.0180309s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+solver took 3.20645s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05
@@ -0,0 +1,56 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.109221s.
+Preconditioner took 0.0286016s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+solver took 0.128301s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05
@@ -0,0 +1,425 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.125661s.
+Preconditioner took 0.06072s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.900577
+   Pass :  1   Iteration :   1  ||B r|| = 0.900577
+   Pass :  1   Iteration :   2  ||B r|| = 0.900434
+   Pass :  1   Iteration :   3  ||B r|| = 0.900408
+   Pass :  1   Iteration :   4  ||B r|| = 0.900243
+   Pass :  1   Iteration :   5  ||B r|| = 0.899912
+   Pass :  1   Iteration :   6  ||B r|| = 0.899901
+   Pass :  1   Iteration :   7  ||B r|| = 0.898453
+   Pass :  1   Iteration :   8  ||B r|| = 0.898147
+   Pass :  1   Iteration :   9  ||B r|| = 0.892867
+   Pass :  1   Iteration :  10  ||B r|| = 0.89046
+   Pass :  1   Iteration :  11  ||B r|| = 0.890149
+   Pass :  1   Iteration :  12  ||B r|| = 0.887881
+   Pass :  1   Iteration :  13  ||B r|| = 0.886497
+   Pass :  1   Iteration :  14  ||B r|| = 0.881958
+   Pass :  1   Iteration :  15  ||B r|| = 0.873768
+   Pass :  1   Iteration :  16  ||B r|| = 0.866676
+   Pass :  1   Iteration :  17  ||B r|| = 0.862158
+   Pass :  1   Iteration :  18  ||B r|| = 0.862121
+   Pass :  1   Iteration :  19  ||B r|| = 0.861983
+   Pass :  1   Iteration :  20  ||B r|| = 0.852531
+   Pass :  1   Iteration :  21  ||B r|| = 0.851407
+   Pass :  1   Iteration :  22  ||B r|| = 0.81114
+   Pass :  1   Iteration :  23  ||B r|| = 0.811092
+   Pass :  1   Iteration :  24  ||B r|| = 0.794531
+   Pass :  1   Iteration :  25  ||B r|| = 0.794531
+   Pass :  1   Iteration :  26  ||B r|| = 0.788509
+   Pass :  1   Iteration :  27  ||B r|| = 0.783442
+   Pass :  1   Iteration :  28  ||B r|| = 0.75365
+   Pass :  1   Iteration :  29  ||B r|| = 0.736124
+   Pass :  1   Iteration :  30  ||B r|| = 0.718001
+   Pass :  1   Iteration :  31  ||B r|| = 0.70199
+   Pass :  1   Iteration :  32  ||B r|| = 0.701983
+   Pass :  1   Iteration :  33  ||B r|| = 0.691506
+   Pass :  1   Iteration :  34  ||B r|| = 0.687431
+   Pass :  1   Iteration :  35  ||B r|| = 0.620939
+   Pass :  1   Iteration :  36  ||B r|| = 0.620787
+   Pass :  1   Iteration :  37  ||B r|| = 0.579878
+   Pass :  1   Iteration :  38  ||B r|| = 0.577254
+   Pass :  1   Iteration :  39  ||B r|| = 0.577153
+   Pass :  1   Iteration :  40  ||B r|| = 0.573348
+   Pass :  1   Iteration :  41  ||B r|| = 0.540128
+   Pass :  1   Iteration :  42  ||B r|| = 0.500686
+   Pass :  1   Iteration :  43  ||B r|| = 0.474183
+   Pass :  1   Iteration :  44  ||B r|| = 0.447715
+   Pass :  1   Iteration :  45  ||B r|| = 0.441645
+   Pass :  1   Iteration :  46  ||B r|| = 0.43763
+   Pass :  1   Iteration :  47  ||B r|| = 0.437304
+   Pass :  1   Iteration :  48  ||B r|| = 0.388192
+   Pass :  1   Iteration :  49  ||B r|| = 0.386414
+   Pass :  1   Iteration :  50  ||B r|| = 0.346785
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.346783
+   Pass :  2   Iteration :  52  ||B r|| = 0.346753
+   Pass :  2   Iteration :  53  ||B r|| = 0.346725
+   Pass :  2   Iteration :  54  ||B r|| = 0.346369
+   Pass :  2   Iteration :  55  ||B r|| = 0.345779
+   Pass :  2   Iteration :  56  ||B r|| = 0.340784
+   Pass :  2   Iteration :  57  ||B r|| = 0.338059
+   Pass :  2   Iteration :  58  ||B r|| = 0.330718
+   Pass :  2   Iteration :  59  ||B r|| = 0.32847
+   Pass :  2   Iteration :  60  ||B r|| = 0.326365
+   Pass :  2   Iteration :  61  ||B r|| = 0.32017
+   Pass :  2   Iteration :  62  ||B r|| = 0.319864
+   Pass :  2   Iteration :  63  ||B r|| = 0.290191
+   Pass :  2   Iteration :  64  ||B r|| = 0.29019
+   Pass :  2   Iteration :  65  ||B r|| = 0.275545
+   Pass :  2   Iteration :  66  ||B r|| = 0.274977
+   Pass :  2   Iteration :  67  ||B r|| = 0.274975
+   Pass :  2   Iteration :  68  ||B r|| = 0.250095
+   Pass :  2   Iteration :  69  ||B r|| = 0.245757
+   Pass :  2   Iteration :  70  ||B r|| = 0.226498
+   Pass :  2   Iteration :  71  ||B r|| = 0.21832
+   Pass :  2   Iteration :  72  ||B r|| = 0.209813
+   Pass :  2   Iteration :  73  ||B r|| = 0.197498
+   Pass :  2   Iteration :  74  ||B r|| = 0.194375
+   Pass :  2   Iteration :  75  ||B r|| = 0.185865
+   Pass :  2   Iteration :  76  ||B r|| = 0.160081
+   Pass :  2   Iteration :  77  ||B r|| = 0.155704
+   Pass :  2   Iteration :  78  ||B r|| = 0.140027
+   Pass :  2   Iteration :  79  ||B r|| = 0.138448
+   Pass :  2   Iteration :  80  ||B r|| = 0.138139
+   Pass :  2   Iteration :  81  ||B r|| = 0.125615
+   Pass :  2   Iteration :  82  ||B r|| = 0.12453
+   Pass :  2   Iteration :  83  ||B r|| = 0.109713
+   Pass :  2   Iteration :  84  ||B r|| = 0.108677
+   Pass :  2   Iteration :  85  ||B r|| = 0.105206
+   Pass :  2   Iteration :  86  ||B r|| = 0.10045
+   Pass :  2   Iteration :  87  ||B r|| = 0.0995337
+   Pass :  2   Iteration :  88  ||B r|| = 0.0927337
+   Pass :  2   Iteration :  89  ||B r|| = 0.0865765
+   Pass :  2   Iteration :  90  ||B r|| = 0.0836921
+   Pass :  2   Iteration :  91  ||B r|| = 0.0777179
+   Pass :  2   Iteration :  92  ||B r|| = 0.0777125
+   Pass :  2   Iteration :  93  ||B r|| = 0.075328
+   Pass :  2   Iteration :  94  ||B r|| = 0.0698781
+   Pass :  2   Iteration :  95  ||B r|| = 0.0695923
+   Pass :  2   Iteration :  96  ||B r|| = 0.0582517
+   Pass :  2   Iteration :  97  ||B r|| = 0.0578877
+   Pass :  2   Iteration :  98  ||B r|| = 0.0509695
+   Pass :  2   Iteration :  99  ||B r|| = 0.0492122
+   Pass :  2   Iteration : 100  ||B r|| = 0.049119
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.0491174
+   Pass :  3   Iteration : 102  ||B r|| = 0.048935
+   Pass :  3   Iteration : 103  ||B r|| = 0.0487952
+   Pass :  3   Iteration : 104  ||B r|| = 0.048271
+   Pass :  3   Iteration : 105  ||B r|| = 0.0456151
+   Pass :  3   Iteration : 106  ||B r|| = 0.0420326
+   Pass :  3   Iteration : 107  ||B r|| = 0.0405407
+   Pass :  3   Iteration : 108  ||B r|| = 0.0376982
+   Pass :  3   Iteration : 109  ||B r|| = 0.0374234
+   Pass :  3   Iteration : 110  ||B r|| = 0.0359602
+   Pass :  3   Iteration : 111  ||B r|| = 0.0336756
+   Pass :  3   Iteration : 112  ||B r|| = 0.0331036
+   Pass :  3   Iteration : 113  ||B r|| = 0.0304233
+   Pass :  3   Iteration : 114  ||B r|| = 0.0303832
+   Pass :  3   Iteration : 115  ||B r|| = 0.0290383
+   Pass :  3   Iteration : 116  ||B r|| = 0.0270094
+   Pass :  3   Iteration : 117  ||B r|| = 0.0269671
+   Pass :  3   Iteration : 118  ||B r|| = 0.0234557
+   Pass :  3   Iteration : 119  ||B r|| = 0.0233749
+   Pass :  3   Iteration : 120  ||B r|| = 0.0222709
+   Pass :  3   Iteration : 121  ||B r|| = 0.0210607
+   Pass :  3   Iteration : 122  ||B r|| = 0.0210189
+   Pass :  3   Iteration : 123  ||B r|| = 0.019523
+   Pass :  3   Iteration : 124  ||B r|| = 0.0190986
+   Pass :  3   Iteration : 125  ||B r|| = 0.0182602
+   Pass :  3   Iteration : 126  ||B r|| = 0.0165908
+   Pass :  3   Iteration : 127  ||B r|| = 0.0165826
+   Pass :  3   Iteration : 128  ||B r|| = 0.0155958
+   Pass :  3   Iteration : 129  ||B r|| = 0.0149154
+   Pass :  3   Iteration : 130  ||B r|| = 0.0148837
+   Pass :  3   Iteration : 131  ||B r|| = 0.0133188
+   Pass :  3   Iteration : 132  ||B r|| = 0.0133041
+   Pass :  3   Iteration : 133  ||B r|| = 0.0126119
+   Pass :  3   Iteration : 134  ||B r|| = 0.012336
+   Pass :  3   Iteration : 135  ||B r|| = 0.0123217
+   Pass :  3   Iteration : 136  ||B r|| = 0.0111051
+   Pass :  3   Iteration : 137  ||B r|| = 0.0110814
+   Pass :  3   Iteration : 138  ||B r|| = 0.0105874
+   Pass :  3   Iteration : 139  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 140  ||B r|| = 0.0104149
+   Pass :  3   Iteration : 141  ||B r|| = 0.00988104
+   Pass :  3   Iteration : 142  ||B r|| = 0.00946548
+   Pass :  3   Iteration : 143  ||B r|| = 0.00898965
+   Pass :  3   Iteration : 144  ||B r|| = 0.00849411
+   Pass :  3   Iteration : 145  ||B r|| = 0.00847611
+   Pass :  3   Iteration : 146  ||B r|| = 0.00791422
+   Pass :  3   Iteration : 147  ||B r|| = 0.00760638
+   Pass :  3   Iteration : 148  ||B r|| = 0.00739417
+   Pass :  3   Iteration : 149  ||B r|| = 0.00658704
+   Pass :  3   Iteration : 150  ||B r|| = 0.00657621
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 0.00657611
+   Pass :  4   Iteration : 152  ||B r|| = 0.00631889
+   Pass :  4   Iteration : 153  ||B r|| = 0.00630107
+   Pass :  4   Iteration : 154  ||B r|| = 0.00628496
+   Pass :  4   Iteration : 155  ||B r|| = 0.00581361
+   Pass :  4   Iteration : 156  ||B r|| = 0.00572566
+   Pass :  4   Iteration : 157  ||B r|| = 0.00558237
+   Pass :  4   Iteration : 158  ||B r|| = 0.00520369
+   Pass :  4   Iteration : 159  ||B r|| = 0.0052025
+   Pass :  4   Iteration : 160  ||B r|| = 0.00487642
+   Pass :  4   Iteration : 161  ||B r|| = 0.00479177
+   Pass :  4   Iteration : 162  ||B r|| = 0.00468477
+   Pass :  4   Iteration : 163  ||B r|| = 0.00440739
+   Pass :  4   Iteration : 164  ||B r|| = 0.00440725
+   Pass :  4   Iteration : 165  ||B r|| = 0.00415237
+   Pass :  4   Iteration : 166  ||B r|| = 0.00404373
+   Pass :  4   Iteration : 167  ||B r|| = 0.00399217
+   Pass :  4   Iteration : 168  ||B r|| = 0.00361744
+   Pass :  4   Iteration : 169  ||B r|| = 0.00361199
+   Pass :  4   Iteration : 170  ||B r|| = 0.00342198
+   Pass :  4   Iteration : 171  ||B r|| = 0.00332275
+   Pass :  4   Iteration : 172  ||B r|| = 0.00328849
+   Pass :  4   Iteration : 173  ||B r|| = 0.00301807
+   Pass :  4   Iteration : 174  ||B r|| = 0.00297077
+   Pass :  4   Iteration : 175  ||B r|| = 0.00278725
+   Pass :  4   Iteration : 176  ||B r|| = 0.00265647
+   Pass :  4   Iteration : 177  ||B r|| = 0.00265138
+   Pass :  4   Iteration : 178  ||B r|| = 0.00249713
+   Pass :  4   Iteration : 179  ||B r|| = 0.0024458
+   Pass :  4   Iteration : 180  ||B r|| = 0.00226749
+   Pass :  4   Iteration : 181  ||B r|| = 0.00211128
+   Pass :  4   Iteration : 182  ||B r|| = 0.00209348
+   Pass :  4   Iteration : 183  ||B r|| = 0.00199424
+   Pass :  4   Iteration : 184  ||B r|| = 0.00190927
+   Pass :  4   Iteration : 185  ||B r|| = 0.00186211
+   Pass :  4   Iteration : 186  ||B r|| = 0.00157145
+   Pass :  4   Iteration : 187  ||B r|| = 0.00157142
+   Pass :  4   Iteration : 188  ||B r|| = 0.00141191
+   Pass :  4   Iteration : 189  ||B r|| = 0.00136095
+   Pass :  4   Iteration : 190  ||B r|| = 0.00133934
+   Pass :  4   Iteration : 191  ||B r|| = 0.00123125
+   Pass :  4   Iteration : 192  ||B r|| = 0.00122694
+   Pass :  4   Iteration : 193  ||B r|| = 0.00112965
+   Pass :  4   Iteration : 194  ||B r|| = 0.00106884
+   Pass :  4   Iteration : 195  ||B r|| = 0.00106156
+   Pass :  4   Iteration : 196  ||B r|| = 0.000979129
+   Pass :  4   Iteration : 197  ||B r|| = 0.000974447
+   Pass :  4   Iteration : 198  ||B r|| = 0.000913577
+   Pass :  4   Iteration : 199  ||B r|| = 0.000824117
+   Pass :  4   Iteration : 200  ||B r|| = 0.000819664
+Restarting...
+   Pass :  5   Iteration : 201  ||B r|| = 0.000819566
+   Pass :  5   Iteration : 202  ||B r|| = 0.000802101
+   Pass :  5   Iteration : 203  ||B r|| = 0.000793705
+   Pass :  5   Iteration : 204  ||B r|| = 0.000779788
+   Pass :  5   Iteration : 205  ||B r|| = 0.000730173
+   Pass :  5   Iteration : 206  ||B r|| = 0.000710072
+   Pass :  5   Iteration : 207  ||B r|| = 0.000686091
+   Pass :  5   Iteration : 208  ||B r|| = 0.000635314
+   Pass :  5   Iteration : 209  ||B r|| = 0.000635226
+   Pass :  5   Iteration : 210  ||B r|| = 0.000604069
+   Pass :  5   Iteration : 211  ||B r|| = 0.000565668
+   Pass :  5   Iteration : 212  ||B r|| = 0.000557792
+   Pass :  5   Iteration : 213  ||B r|| = 0.000515749
+   Pass :  5   Iteration : 214  ||B r|| = 0.000513034
+   Pass :  5   Iteration : 215  ||B r|| = 0.000481894
+   Pass :  5   Iteration : 216  ||B r|| = 0.000451544
+   Pass :  5   Iteration : 217  ||B r|| = 0.00044852
+   Pass :  5   Iteration : 218  ||B r|| = 0.000393422
+   Pass :  5   Iteration : 219  ||B r|| = 0.000381413
+   Pass :  5   Iteration : 220  ||B r|| = 0.000361236
+   Pass :  5   Iteration : 221  ||B r|| = 0.000336538
+   Pass :  5   Iteration : 222  ||B r|| = 0.000336118
+   Pass :  5   Iteration : 223  ||B r|| = 0.000320216
+   Pass :  5   Iteration : 224  ||B r|| = 0.000311681
+   Pass :  5   Iteration : 225  ||B r|| = 0.000300208
+   Pass :  5   Iteration : 226  ||B r|| = 0.000280096
+   Pass :  5   Iteration : 227  ||B r|| = 0.000280017
+   Pass :  5   Iteration : 228  ||B r|| = 0.000265884
+   Pass :  5   Iteration : 229  ||B r|| = 0.000254531
+   Pass :  5   Iteration : 230  ||B r|| = 0.000253443
+   Pass :  5   Iteration : 231  ||B r|| = 0.000232182
+   Pass :  5   Iteration : 232  ||B r|| = 0.000231948
+   Pass :  5   Iteration : 233  ||B r|| = 0.000219717
+   Pass :  5   Iteration : 234  ||B r|| = 0.000210106
+   Pass :  5   Iteration : 235  ||B r|| = 0.000208378
+   Pass :  5   Iteration : 236  ||B r|| = 0.000192791
+   Pass :  5   Iteration : 237  ||B r|| = 0.000191389
+   Pass :  5   Iteration : 238  ||B r|| = 0.000181136
+   Pass :  5   Iteration : 239  ||B r|| = 0.000173082
+   Pass :  5   Iteration : 240  ||B r|| = 0.000172178
+   Pass :  5   Iteration : 241  ||B r|| = 0.000163582
+   Pass :  5   Iteration : 242  ||B r|| = 0.000160314
+   Pass :  5   Iteration : 243  ||B r|| = 0.000154194
+   Pass :  5   Iteration : 244  ||B r|| = 0.000142641
+   Pass :  5   Iteration : 245  ||B r|| = 0.000142245
+   Pass :  5   Iteration : 246  ||B r|| = 0.000135685
+   Pass :  5   Iteration : 247  ||B r|| = 0.000134161
+   Pass :  5   Iteration : 248  ||B r|| = 0.00013191
+   Pass :  5   Iteration : 249  ||B r|| = 0.00011789
+   Pass :  5   Iteration : 250  ||B r|| = 0.000117448
+Restarting...
+   Pass :  6   Iteration : 251  ||B r|| = 0.000117443
+   Pass :  6   Iteration : 252  ||B r|| = 0.000111241
+   Pass :  6   Iteration : 253  ||B r|| = 0.000111092
+   Pass :  6   Iteration : 254  ||B r|| = 0.000111075
+   Pass :  6   Iteration : 255  ||B r|| = 0.000101403
+   Pass :  6   Iteration : 256  ||B r|| = 0.000100984
+   Pass :  6   Iteration : 257  ||B r|| = 9.60892e-05
+   Pass :  6   Iteration : 258  ||B r|| = 9.16341e-05
+   Pass :  6   Iteration : 259  ||B r|| = 9.1184e-05
+   Pass :  6   Iteration : 260  ||B r|| = 8.57519e-05
+   Pass :  6   Iteration : 261  ||B r|| = 8.49038e-05
+   Pass :  6   Iteration : 262  ||B r|| = 8.25868e-05
+   Pass :  6   Iteration : 263  ||B r|| = 7.84909e-05
+   Pass :  6   Iteration : 264  ||B r|| = 7.84882e-05
+   Pass :  6   Iteration : 265  ||B r|| = 7.17122e-05
+   Pass :  6   Iteration : 266  ||B r|| = 7.06387e-05
+   Pass :  6   Iteration : 267  ||B r|| = 6.88435e-05
+   Pass :  6   Iteration : 268  ||B r|| = 6.51125e-05
+   Pass :  6   Iteration : 269  ||B r|| = 6.51119e-05
+   Pass :  6   Iteration : 270  ||B r|| = 6.11726e-05
+   Pass :  6   Iteration : 271  ||B r|| = 5.95685e-05
+   Pass :  6   Iteration : 272  ||B r|| = 5.69221e-05
+   Pass :  6   Iteration : 273  ||B r|| = 5.31348e-05
+   Pass :  6   Iteration : 274  ||B r|| = 5.29896e-05
+   Pass :  6   Iteration : 275  ||B r|| = 5.06603e-05
+   Pass :  6   Iteration : 276  ||B r|| = 4.77003e-05
+   Pass :  6   Iteration : 277  ||B r|| = 4.69104e-05
+   Pass :  6   Iteration : 278  ||B r|| = 4.35213e-05
+   Pass :  6   Iteration : 279  ||B r|| = 4.34584e-05
+   Pass :  6   Iteration : 280  ||B r|| = 4.13801e-05
+   Pass :  6   Iteration : 281  ||B r|| = 3.80137e-05
+   Pass :  6   Iteration : 282  ||B r|| = 3.73519e-05
+   Pass :  6   Iteration : 283  ||B r|| = 3.40659e-05
+   Pass :  6   Iteration : 284  ||B r|| = 3.35469e-05
+   Pass :  6   Iteration : 285  ||B r|| = 3.24228e-05
+   Pass :  6   Iteration : 286  ||B r|| = 2.82691e-05
+   Pass :  6   Iteration : 287  ||B r|| = 2.82415e-05
+   Pass :  6   Iteration : 288  ||B r|| = 2.4949e-05
+   Pass :  6   Iteration : 289  ||B r|| = 2.42639e-05
+   Pass :  6   Iteration : 290  ||B r|| = 2.35408e-05
+   Pass :  6   Iteration : 291  ||B r|| = 2.19407e-05
+   Pass :  6   Iteration : 292  ||B r|| = 2.19132e-05
+   Pass :  6   Iteration : 293  ||B r|| = 2.03845e-05
+   Pass :  6   Iteration : 294  ||B r|| = 1.92894e-05
+   Pass :  6   Iteration : 295  ||B r|| = 1.89518e-05
+   Pass :  6   Iteration : 296  ||B r|| = 1.72028e-05
+   Pass :  6   Iteration : 297  ||B r|| = 1.71928e-05
+   Pass :  6   Iteration : 298  ||B r|| = 1.63643e-05
+   Pass :  6   Iteration : 299  ||B r|| = 1.56163e-05
+   Pass :  6   Iteration : 300  ||B r|| = 1.54755e-05
+Restarting...
+   Pass :  7   Iteration : 301  ||B r|| = 1.54724e-05
+   Pass :  7   Iteration : 302  ||B r|| = 1.53376e-05
+   Pass :  7   Iteration : 303  ||B r|| = 1.50205e-05
+   Pass :  7   Iteration : 304  ||B r|| = 1.47195e-05
+   Pass :  7   Iteration : 305  ||B r|| = 1.34414e-05
+   Pass :  7   Iteration : 306  ||B r|| = 1.30372e-05
+   Pass :  7   Iteration : 307  ||B r|| = 1.26163e-05
+   Pass :  7   Iteration : 308  ||B r|| = 1.17954e-05
+   Pass :  7   Iteration : 309  ||B r|| = 1.17113e-05
+   Pass :  7   Iteration : 310  ||B r|| = 1.12938e-05
+   Pass :  7   Iteration : 311  ||B r|| = 1.04865e-05
+   Pass :  7   Iteration : 312  ||B r|| = 1.03571e-05
+   Pass :  7   Iteration : 313  ||B r|| = 9.56454e-06
+   Pass :  7   Iteration : 314  ||B r|| = 9.44709e-06
+   Pass :  7   Iteration : 315  ||B r|| = 9.02016e-06
+   Pass :  7   Iteration : 316  ||B r|| = 8.27621e-06
+   Pass :  7   Iteration : 317  ||B r|| = 8.26159e-06
+   Pass :  7   Iteration : 318  ||B r|| = 7.18002e-06
+   Pass :  7   Iteration : 319  ||B r|| = 6.95003e-06
+   Pass :  7   Iteration : 320  ||B r|| = 6.73497e-06
+   Pass :  7   Iteration : 321  ||B r|| = 6.25227e-06
+   Pass :  7   Iteration : 322  ||B r|| = 6.24358e-06
+   Pass :  7   Iteration : 323  ||B r|| = 5.90685e-06
+   Pass :  7   Iteration : 324  ||B r|| = 5.69217e-06
+   Pass :  7   Iteration : 325  ||B r|| = 5.59816e-06
+   Pass :  7   Iteration : 326  ||B r|| = 5.19767e-06
+   Pass :  7   Iteration : 327  ||B r|| = 5.18732e-06
+   Pass :  7   Iteration : 328  ||B r|| = 4.978e-06
+   Pass :  7   Iteration : 329  ||B r|| = 4.61108e-06
+   Pass :  7   Iteration : 330  ||B r|| = 4.60926e-06
+   Pass :  7   Iteration : 331  ||B r|| = 4.23343e-06
+   Pass :  7   Iteration : 332  ||B r|| = 4.23029e-06
+   Pass :  7   Iteration : 333  ||B r|| = 4.01039e-06
+   Pass :  7   Iteration : 334  ||B r|| = 3.86812e-06
+   Pass :  7   Iteration : 335  ||B r|| = 3.86282e-06
+   Pass :  7   Iteration : 336  ||B r|| = 3.60676e-06
+   Pass :  7   Iteration : 337  ||B r|| = 3.53527e-06
+   Pass :  7   Iteration : 338  ||B r|| = 3.33113e-06
+   Pass :  7   Iteration : 339  ||B r|| = 3.15944e-06
+   Pass :  7   Iteration : 340  ||B r|| = 3.14716e-06
+   Pass :  7   Iteration : 341  ||B r|| = 2.97802e-06
+   Pass :  7   Iteration : 342  ||B r|| = 2.95139e-06
+   Pass :  7   Iteration : 343  ||B r|| = 2.86922e-06
+   Pass :  7   Iteration : 344  ||B r|| = 2.65035e-06
+   Pass :  7   Iteration : 345  ||B r|| = 2.64952e-06
+   Pass :  7   Iteration : 346  ||B r|| = 2.48989e-06
+   Pass :  7   Iteration : 347  ||B r|| = 2.42609e-06
+   Pass :  7   Iteration : 348  ||B r|| = 2.35361e-06
+   Pass :  7   Iteration : 349  ||B r|| = 2.0977e-06
+   Pass :  7   Iteration : 350  ||B r|| = 2.0743e-06
+Restarting...
+   Pass :  8   Iteration : 351  ||B r|| = 2.074e-06
+   Pass :  8   Iteration : 352  ||B r|| = 1.9458e-06
+   Pass :  8   Iteration : 353  ||B r|| = 1.91268e-06
+   Pass :  8   Iteration : 354  ||B r|| = 1.9109e-06
+   Pass :  8   Iteration : 355  ||B r|| = 1.71169e-06
+   Pass :  8   Iteration : 356  ||B r|| = 1.70656e-06
+   Pass :  8   Iteration : 357  ||B r|| = 1.61858e-06
+   Pass :  8   Iteration : 358  ||B r|| = 1.53201e-06
+   Pass :  8   Iteration : 359  ||B r|| = 1.52511e-06
+   Pass :  8   Iteration : 360  ||B r|| = 1.4294e-06
+   Pass :  8   Iteration : 361  ||B r|| = 1.40067e-06
+   Pass :  8   Iteration : 362  ||B r|| = 1.35966e-06
+   Pass :  8   Iteration : 363  ||B r|| = 1.29997e-06
+   Pass :  8   Iteration : 364  ||B r|| = 1.29896e-06
+   Pass :  8   Iteration : 365  ||B r|| = 1.192e-06
+   Pass :  8   Iteration : 366  ||B r|| = 1.17842e-06
+   Pass :  8   Iteration : 367  ||B r|| = 1.14545e-06
+   Pass :  8   Iteration : 368  ||B r|| = 1.08481e-06
+   Pass :  8   Iteration : 369  ||B r|| = 1.08408e-06
+   Pass :  8   Iteration : 370  ||B r|| = 1.01158e-06
+   Pass :  8   Iteration : 371  ||B r|| = 9.87365e-07
+   Pass :  8   Iteration : 372  ||B r|| = 9.53571e-07
+   Pass :  8   Iteration : 373  ||B r|| = 9.02865e-07
+   Pass :  8   Iteration : 374  ||B r|| = 9.02529e-07
+   Pass :  8   Iteration : 375  ||B r|| = 8.35677e-07
+GMRES+GS converged in 375 iterations with a residual norm of 8.35677e-07.
+solver took 2.17952s.
+|| q_h - q_ex || / || q_ex || = 5.07159e-05
+|| t_h - t_ex || / || t_ex || = 2.61662e-05
@@ -0,0 +1,57 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.141771s.
+Preconditioner took 0.0573248s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+solver took 0.0894688s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05
@@ -0,0 +1,80 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.000134119s.
+***********************************************************
+dim(W) = 1024
+***********************************************************
+Assembly took 0.136547s.
+Preconditioner took 1.374e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.940451
+   Pass :  1   Iteration :   1  ||B r|| = 0.842832
+   Pass :  1   Iteration :   2  ||B r|| = 0.725223
+   Pass :  1   Iteration :   3  ||B r|| = 0.522084
+   Pass :  1   Iteration :   4  ||B r|| = 0.445295
+   Pass :  1   Iteration :   5  ||B r|| = 0.355162
+   Pass :  1   Iteration :   6  ||B r|| = 0.297819
+   Pass :  1   Iteration :   7  ||B r|| = 0.238349
+   Pass :  1   Iteration :   8  ||B r|| = 0.192402
+   Pass :  1   Iteration :   9  ||B r|| = 0.143872
+   Pass :  1   Iteration :  10  ||B r|| = 0.0949139
+   Pass :  1   Iteration :  11  ||B r|| = 0.0606282
+   Pass :  1   Iteration :  12  ||B r|| = 0.0414828
+   Pass :  1   Iteration :  13  ||B r|| = 0.0284458
+   Pass :  1   Iteration :  14  ||B r|| = 0.0188111
+   Pass :  1   Iteration :  15  ||B r|| = 0.0114118
+   Pass :  1   Iteration :  16  ||B r|| = 0.00590335
+   Pass :  1   Iteration :  17  ||B r|| = 0.00348072
+   Pass :  1   Iteration :  18  ||B r|| = 0.00219975
+   Pass :  1   Iteration :  19  ||B r|| = 0.00152431
+   Pass :  1   Iteration :  20  ||B r|| = 0.00105872
+   Pass :  1   Iteration :  21  ||B r|| = 0.000589053
+   Pass :  1   Iteration :  22  ||B r|| = 0.000294206
+   Pass :  1   Iteration :  23  ||B r|| = 0.00017458
+   Pass :  1   Iteration :  24  ||B r|| = 0.000108035
+   Pass :  1   Iteration :  25  ||B r|| = 7.75177e-05
+   Pass :  1   Iteration :  26  ||B r|| = 5.53841e-05
+   Pass :  1   Iteration :  27  ||B r|| = 4.10593e-05
+   Pass :  1   Iteration :  28  ||B r|| = 2.95403e-05
+   Pass :  1   Iteration :  29  ||B r|| = 2.27173e-05
+   Pass :  1   Iteration :  30  ||B r|| = 1.53028e-05
+   Pass :  1   Iteration :  31  ||B r|| = 9.45566e-06
+   Pass :  1   Iteration :  32  ||B r|| = 5.05412e-06
+   Pass :  1   Iteration :  33  ||B r|| = 2.90871e-06
+   Pass :  1   Iteration :  34  ||B r|| = 1.67544e-06
+   Pass :  1   Iteration :  35  ||B r|| = 9.57804e-07
+   Pass :  1   Iteration :  36  ||B r|| = 5.39153e-07
+GMRES+GS converged in 36 iterations with a residual norm of 5.39153e-07.
+solver took 0.0189671s.
+|| q_h - q_ex || / || q_ex || = 5.07039e-05
+|| t_h - t_ex || / || t_ex || = 2.61565e-05
@@ -0,0 +1,45 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --reduction
+   --no-hybridization
+   --no-nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Reduction init took 0.00110061s.
+***********************************************************
+dim(W) = 1024
+***********************************************************
+Assembly took 0.134487s.
+Preconditioner took 0.00721732s.
+   Pass :  1   Iteration :   0  ||B r|| = 46.4068
+   Pass :  1   Iteration :   1  ||B r|| = 6.79805e-14
+GMRES+UMFPack converged in 1 iterations with a residual norm of 6.79805e-14.
+solver took 0.00359861s.
+|| q_h - q_ex || / || q_ex || = 5.07127e-05
+|| t_h - t_ex || / || t_ex || = 2.6156e-05
@@ -0,0 +1,52 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2048
+dim(W) = 1024
+dim(V+W) = 3072
+***********************************************************
+Assembly took 0.140492s.
+Preconditioner took 0.0152542s.
+   Pass :  1   Iteration :   0  ||B r|| = 34.0948
+   Pass :  1   Iteration :   1  ||B r|| = 34.0948
+   Pass :  1   Iteration :   2  ||B r|| = 0.0882945
+   Pass :  1   Iteration :   3  ||B r|| = 0.0197291
+   Pass :  1   Iteration :   4  ||B r|| = 0.0182002
+   Pass :  1   Iteration :   5  ||B r|| = 0.00466911
+   Pass :  1   Iteration :   6  ||B r|| = 0.00191841
+   Pass :  1   Iteration :   7  ||B r|| = 0.00153367
+   Pass :  1   Iteration :   8  ||B r|| = 0.00108376
+   Pass :  1   Iteration :   9  ||B r|| = 0.00106531
+   Pass :  1   Iteration :  10  ||B r|| = 0.000264455
+   Pass :  1   Iteration :  11  ||B r|| = 9.66463e-05
+   Pass :  1   Iteration :  12  ||B r|| = 9.54134e-05
+   Pass :  1   Iteration :  13  ||B r|| = 4.64374e-05
+   Pass :  1   Iteration :  14  ||B r|| = 2.53717e-05
+GMRES+UMFPack converged in 14 iterations with a residual norm of 2.53717e-05.
+GMRES solver took 0.0206901s.
+|| q_h - q_ex || / || q_ex || = 5.06633e-05
+|| t_h - t_ex || / || t_ex || = 2.61371e-05
@@ -0,0 +1,63 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0342793s.
+Preconditioner took 1.2454e-05s.
+   Pass :  1   Iteration :   0  ||B r|| = 1.36532
+   Pass :  1   Iteration :   1  ||B r|| = 0.999065
+   Pass :  1   Iteration :   2  ||B r|| = 0.687902
+   Pass :  1   Iteration :   3  ||B r|| = 0.493004
+   Pass :  1   Iteration :   4  ||B r|| = 0.376497
+   Pass :  1   Iteration :   5  ||B r|| = 0.282937
+   Pass :  1   Iteration :   6  ||B r|| = 0.178236
+   Pass :  1   Iteration :   7  ||B r|| = 0.108367
+   Pass :  1   Iteration :   8  ||B r|| = 0.0611648
+   Pass :  1   Iteration :   9  ||B r|| = 0.0306066
+   Pass :  1   Iteration :  10  ||B r|| = 0.0182875
+   Pass :  1   Iteration :  11  ||B r|| = 0.00795556
+   Pass :  1   Iteration :  12  ||B r|| = 0.00414347
+   Pass :  1   Iteration :  13  ||B r|| = 0.00181918
+   Pass :  1   Iteration :  14  ||B r|| = 0.00121887
+   Pass :  1   Iteration :  15  ||B r|| = 0.000633013
+   Pass :  1   Iteration :  16  ||B r|| = 0.000336192
+   Pass :  1   Iteration :  17  ||B r|| = 0.000190052
+   Pass :  1   Iteration :  18  ||B r|| = 0.000142776
+   Pass :  1   Iteration :  19  ||B r|| = 8.08217e-05
+   Pass :  1   Iteration :  20  ||B r|| = 4.04241e-05
+   Pass :  1   Iteration :  21  ||B r|| = 1.64814e-05
+   Pass :  1   Iteration :  22  ||B r|| = 9.59614e-06
+   Pass :  1   Iteration :  23  ||B r|| = 2.9853e-06
+   Pass :  1   Iteration :  24  ||B r|| = 1.56186e-06
+   Pass :  1   Iteration :  25  ||B r|| = 4.80159e-07
+GMRES+GS converged in 25 iterations with a residual norm of 4.80159e-07.
+GMRES solver took 0.00317834s.
+|| q_h - q_ex || / || q_ex || = 3.55334e-07
+|| t_h - t_ex || / || t_ex || = 1.76357e-07
@@ -0,0 +1,236 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0541371s.
+Preconditioner took 0.129626s.
+   Pass :  1   Iteration :   0  ||B r|| = 0.828288
+   Pass :  1   Iteration :   1  ||B r|| = 0.828288
+   Pass :  1   Iteration :   2  ||B r|| = 0.780392
+   Pass :  1   Iteration :   3  ||B r|| = 0.775902
+   Pass :  1   Iteration :   4  ||B r|| = 0.718999
+   Pass :  1   Iteration :   5  ||B r|| = 0.712741
+   Pass :  1   Iteration :   6  ||B r|| = 0.709216
+   Pass :  1   Iteration :   7  ||B r|| = 0.699357
+   Pass :  1   Iteration :   8  ||B r|| = 0.685558
+   Pass :  1   Iteration :   9  ||B r|| = 0.624758
+   Pass :  1   Iteration :  10  ||B r|| = 0.61651
+   Pass :  1   Iteration :  11  ||B r|| = 0.491672
+   Pass :  1   Iteration :  12  ||B r|| = 0.490509
+   Pass :  1   Iteration :  13  ||B r|| = 0.43273
+   Pass :  1   Iteration :  14  ||B r|| = 0.432532
+   Pass :  1   Iteration :  15  ||B r|| = 0.391607
+   Pass :  1   Iteration :  16  ||B r|| = 0.387505
+   Pass :  1   Iteration :  17  ||B r|| = 0.369287
+   Pass :  1   Iteration :  18  ||B r|| = 0.349727
+   Pass :  1   Iteration :  19  ||B r|| = 0.344534
+   Pass :  1   Iteration :  20  ||B r|| = 0.308102
+   Pass :  1   Iteration :  21  ||B r|| = 0.307918
+   Pass :  1   Iteration :  22  ||B r|| = 0.275424
+   Pass :  1   Iteration :  23  ||B r|| = 0.275336
+   Pass :  1   Iteration :  24  ||B r|| = 0.241166
+   Pass :  1   Iteration :  25  ||B r|| = 0.236098
+   Pass :  1   Iteration :  26  ||B r|| = 0.220482
+   Pass :  1   Iteration :  27  ||B r|| = 0.209195
+   Pass :  1   Iteration :  28  ||B r|| = 0.203284
+   Pass :  1   Iteration :  29  ||B r|| = 0.184134
+   Pass :  1   Iteration :  30  ||B r|| = 0.183885
+   Pass :  1   Iteration :  31  ||B r|| = 0.158572
+   Pass :  1   Iteration :  32  ||B r|| = 0.15785
+   Pass :  1   Iteration :  33  ||B r|| = 0.128252
+   Pass :  1   Iteration :  34  ||B r|| = 0.121277
+   Pass :  1   Iteration :  35  ||B r|| = 0.105019
+   Pass :  1   Iteration :  36  ||B r|| = 0.0877653
+   Pass :  1   Iteration :  37  ||B r|| = 0.0857034
+   Pass :  1   Iteration :  38  ||B r|| = 0.0695776
+   Pass :  1   Iteration :  39  ||B r|| = 0.0693421
+   Pass :  1   Iteration :  40  ||B r|| = 0.060764
+   Pass :  1   Iteration :  41  ||B r|| = 0.0583294
+   Pass :  1   Iteration :  42  ||B r|| = 0.0513009
+   Pass :  1   Iteration :  43  ||B r|| = 0.046381
+   Pass :  1   Iteration :  44  ||B r|| = 0.0446401
+   Pass :  1   Iteration :  45  ||B r|| = 0.0351366
+   Pass :  1   Iteration :  46  ||B r|| = 0.0350703
+   Pass :  1   Iteration :  47  ||B r|| = 0.0285254
+   Pass :  1   Iteration :  48  ||B r|| = 0.0275435
+   Pass :  1   Iteration :  49  ||B r|| = 0.0233101
+   Pass :  1   Iteration :  50  ||B r|| = 0.0205522
+Restarting...
+   Pass :  2   Iteration :  51  ||B r|| = 0.0201743
+   Pass :  2   Iteration :  52  ||B r|| = 0.0178036
+   Pass :  2   Iteration :  53  ||B r|| = 0.0177657
+   Pass :  2   Iteration :  54  ||B r|| = 0.0155379
+   Pass :  2   Iteration :  55  ||B r|| = 0.0145024
+   Pass :  2   Iteration :  56  ||B r|| = 0.0129692
+   Pass :  2   Iteration :  57  ||B r|| = 0.0111895
+   Pass :  2   Iteration :  58  ||B r|| = 0.0106264
+   Pass :  2   Iteration :  59  ||B r|| = 0.00883739
+   Pass :  2   Iteration :  60  ||B r|| = 0.00881869
+   Pass :  2   Iteration :  61  ||B r|| = 0.00734547
+   Pass :  2   Iteration :  62  ||B r|| = 0.00727023
+   Pass :  2   Iteration :  63  ||B r|| = 0.00664677
+   Pass :  2   Iteration :  64  ||B r|| = 0.00606592
+   Pass :  2   Iteration :  65  ||B r|| = 0.00584805
+   Pass :  2   Iteration :  66  ||B r|| = 0.00471596
+   Pass :  2   Iteration :  67  ||B r|| = 0.00467814
+   Pass :  2   Iteration :  68  ||B r|| = 0.00343373
+   Pass :  2   Iteration :  69  ||B r|| = 0.0034201
+   Pass :  2   Iteration :  70  ||B r|| = 0.00280534
+   Pass :  2   Iteration :  71  ||B r|| = 0.00270379
+   Pass :  2   Iteration :  72  ||B r|| = 0.0025783
+   Pass :  2   Iteration :  73  ||B r|| = 0.0022472
+   Pass :  2   Iteration :  74  ||B r|| = 0.00221863
+   Pass :  2   Iteration :  75  ||B r|| = 0.00186269
+   Pass :  2   Iteration :  76  ||B r|| = 0.00186179
+   Pass :  2   Iteration :  77  ||B r|| = 0.00160985
+   Pass :  2   Iteration :  78  ||B r|| = 0.00160018
+   Pass :  2   Iteration :  79  ||B r|| = 0.00148445
+   Pass :  2   Iteration :  80  ||B r|| = 0.00141886
+   Pass :  2   Iteration :  81  ||B r|| = 0.00139003
+   Pass :  2   Iteration :  82  ||B r|| = 0.00125305
+   Pass :  2   Iteration :  83  ||B r|| = 0.00124651
+   Pass :  2   Iteration :  84  ||B r|| = 0.00111105
+   Pass :  2   Iteration :  85  ||B r|| = 0.00110481
+   Pass :  2   Iteration :  86  ||B r|| = 0.001019
+   Pass :  2   Iteration :  87  ||B r|| = 0.000986979
+   Pass :  2   Iteration :  88  ||B r|| = 0.000943191
+   Pass :  2   Iteration :  89  ||B r|| = 0.000887917
+   Pass :  2   Iteration :  90  ||B r|| = 0.000878207
+   Pass :  2   Iteration :  91  ||B r|| = 0.000792828
+   Pass :  2   Iteration :  92  ||B r|| = 0.000792314
+   Pass :  2   Iteration :  93  ||B r|| = 0.00067918
+   Pass :  2   Iteration :  94  ||B r|| = 0.000661497
+   Pass :  2   Iteration :  95  ||B r|| = 0.000607798
+   Pass :  2   Iteration :  96  ||B r|| = 0.000585659
+   Pass :  2   Iteration :  97  ||B r|| = 0.000575458
+   Pass :  2   Iteration :  98  ||B r|| = 0.000536371
+   Pass :  2   Iteration :  99  ||B r|| = 0.000533329
+   Pass :  2   Iteration : 100  ||B r|| = 0.000476474
+Restarting...
+   Pass :  3   Iteration : 101  ||B r|| = 0.000476389
+   Pass :  3   Iteration : 102  ||B r|| = 0.000450568
+   Pass :  3   Iteration : 103  ||B r|| = 0.00044946
+   Pass :  3   Iteration : 104  ||B r|| = 0.000448032
+   Pass :  3   Iteration : 105  ||B r|| = 0.000436727
+   Pass :  3   Iteration : 106  ||B r|| = 0.000433054
+   Pass :  3   Iteration : 107  ||B r|| = 0.000384572
+   Pass :  3   Iteration : 108  ||B r|| = 0.000384151
+   Pass :  3   Iteration : 109  ||B r|| = 0.000326889
+   Pass :  3   Iteration : 110  ||B r|| = 0.000320214
+   Pass :  3   Iteration : 111  ||B r|| = 0.000295531
+   Pass :  3   Iteration : 112  ||B r|| = 0.00028017
+   Pass :  3   Iteration : 113  ||B r|| = 0.000271805
+   Pass :  3   Iteration : 114  ||B r|| = 0.000253182
+   Pass :  3   Iteration : 115  ||B r|| = 0.000251705
+   Pass :  3   Iteration : 116  ||B r|| = 0.000224202
+   Pass :  3   Iteration : 117  ||B r|| = 0.00022401
+   Pass :  3   Iteration : 118  ||B r|| = 0.000201373
+   Pass :  3   Iteration : 119  ||B r|| = 0.000195487
+   Pass :  3   Iteration : 120  ||B r|| = 0.000178312
+   Pass :  3   Iteration : 121  ||B r|| = 0.000163707
+   Pass :  3   Iteration : 122  ||B r|| = 0.000159212
+   Pass :  3   Iteration : 123  ||B r|| = 0.000143717
+   Pass :  3   Iteration : 124  ||B r|| = 0.000142938
+   Pass :  3   Iteration : 125  ||B r|| = 0.000129618
+   Pass :  3   Iteration : 126  ||B r|| = 0.000128535
+   Pass :  3   Iteration : 127  ||B r|| = 0.000120081
+   Pass :  3   Iteration : 128  ||B r|| = 0.000114142
+   Pass :  3   Iteration : 129  ||B r|| = 0.000109227
+   Pass :  3   Iteration : 130  ||B r|| = 9.74187e-05
+   Pass :  3   Iteration : 131  ||B r|| = 9.41802e-05
+   Pass :  3   Iteration : 132  ||B r|| = 7.97569e-05
+   Pass :  3   Iteration : 133  ||B r|| = 7.97329e-05
+   Pass :  3   Iteration : 134  ||B r|| = 6.96569e-05
+   Pass :  3   Iteration : 135  ||B r|| = 6.80129e-05
+   Pass :  3   Iteration : 136  ||B r|| = 6.39905e-05
+   Pass :  3   Iteration : 137  ||B r|| = 5.48303e-05
+   Pass :  3   Iteration : 138  ||B r|| = 5.33803e-05
+   Pass :  3   Iteration : 139  ||B r|| = 4.51005e-05
+   Pass :  3   Iteration : 140  ||B r|| = 4.47538e-05
+   Pass :  3   Iteration : 141  ||B r|| = 3.79739e-05
+   Pass :  3   Iteration : 142  ||B r|| = 3.79237e-05
+   Pass :  3   Iteration : 143  ||B r|| = 3.34755e-05
+   Pass :  3   Iteration : 144  ||B r|| = 3.19968e-05
+   Pass :  3   Iteration : 145  ||B r|| = 3.00248e-05
+   Pass :  3   Iteration : 146  ||B r|| = 2.43567e-05
+   Pass :  3   Iteration : 147  ||B r|| = 2.40027e-05
+   Pass :  3   Iteration : 148  ||B r|| = 1.75885e-05
+   Pass :  3   Iteration : 149  ||B r|| = 1.74341e-05
+   Pass :  3   Iteration : 150  ||B r|| = 1.38964e-05
+Restarting...
+   Pass :  4   Iteration : 151  ||B r|| = 1.33084e-05
+   Pass :  4   Iteration : 152  ||B r|| = 1.25291e-05
+   Pass :  4   Iteration : 153  ||B r|| = 1.15613e-05
+   Pass :  4   Iteration : 154  ||B r|| = 1.15039e-05
+   Pass :  4   Iteration : 155  ||B r|| = 8.97445e-06
+   Pass :  4   Iteration : 156  ||B r|| = 8.93619e-06
+   Pass :  4   Iteration : 157  ||B r|| = 7.17725e-06
+   Pass :  4   Iteration : 158  ||B r|| = 7.03949e-06
+   Pass :  4   Iteration : 159  ||B r|| = 6.28998e-06
+   Pass :  4   Iteration : 160  ||B r|| = 5.80418e-06
+   Pass :  4   Iteration : 161  ||B r|| = 5.6565e-06
+   Pass :  4   Iteration : 162  ||B r|| = 4.98291e-06
+   Pass :  4   Iteration : 163  ||B r|| = 4.97198e-06
+   Pass :  4   Iteration : 164  ||B r|| = 4.1327e-06
+   Pass :  4   Iteration : 165  ||B r|| = 4.04729e-06
+   Pass :  4   Iteration : 166  ||B r|| = 3.41458e-06
+   Pass :  4   Iteration : 167  ||B r|| = 3.2682e-06
+   Pass :  4   Iteration : 168  ||B r|| = 3.07084e-06
+   Pass :  4   Iteration : 169  ||B r|| = 2.6426e-06
+   Pass :  4   Iteration : 170  ||B r|| = 2.63354e-06
+   Pass :  4   Iteration : 171  ||B r|| = 2.17891e-06
+   Pass :  4   Iteration : 172  ||B r|| = 2.15133e-06
+   Pass :  4   Iteration : 173  ||B r|| = 1.91418e-06
+   Pass :  4   Iteration : 174  ||B r|| = 1.87277e-06
+   Pass :  4   Iteration : 175  ||B r|| = 1.75707e-06
+   Pass :  4   Iteration : 176  ||B r|| = 1.66039e-06
+   Pass :  4   Iteration : 177  ||B r|| = 1.62259e-06
+   Pass :  4   Iteration : 178  ||B r|| = 1.51352e-06
+   Pass :  4   Iteration : 179  ||B r|| = 1.51341e-06
+   Pass :  4   Iteration : 180  ||B r|| = 1.35973e-06
+   Pass :  4   Iteration : 181  ||B r|| = 1.34071e-06
+   Pass :  4   Iteration : 182  ||B r|| = 1.2227e-06
+   Pass :  4   Iteration : 183  ||B r|| = 1.16459e-06
+   Pass :  4   Iteration : 184  ||B r|| = 1.10473e-06
+   Pass :  4   Iteration : 185  ||B r|| = 9.95649e-07
+   Pass :  4   Iteration : 186  ||B r|| = 9.93491e-07
+   Pass :  4   Iteration : 187  ||B r|| = 9.20855e-07
+   Pass :  4   Iteration : 188  ||B r|| = 9.17534e-07
+   Pass :  4   Iteration : 189  ||B r|| = 8.48816e-07
+   Pass :  4   Iteration : 190  ||B r|| = 8.13729e-07
+GMRES+GS converged in 190 iterations with a residual norm of 8.13729e-07.
+solver took 1.79382s.
+|| q_h - q_ex || / || q_ex || = 1.02359e-06
+|| t_h - t_ex || / || t_ex || = 1.03461e-06
@@ -0,0 +1,47 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --nonlinear-diffusion
+   --hdg_scheme 1
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.0474844s.
+Preconditioner took 0.140224s.
+   Pass :  1   Iteration :   0  ||B r|| = 41.2501
+   Pass :  1   Iteration :   1  ||B r|| = 41.2501
+   Pass :  1   Iteration :   2  ||B r|| = 0.000174926
+   Pass :  1   Iteration :   3  ||B r|| = 4.73276e-05
+   Pass :  1   Iteration :   4  ||B r|| = 5.87823e-06
+GMRES+UMFPack converged in 4 iterations with a residual norm of 5.87823e-06.
+solver took 0.0465522s.
+|| q_h - q_ex || / || q_ex || = 3.02391e-07
+|| t_h - t_ex || / || t_ex || = 1.63476e-07
@@ -0,0 +1,42 @@
+Options used:
+   --mesh 
+   --ncells-x 8
+   --ncells-y 8
+   --size-x 1
+   --size-y 1
+   --order 3
+   --no-discontinuous
+   --centered
+   --problem 1
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-hybridization
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+***********************************************************
+dim(V) = 2112
+dim(W) = 1024
+dim(V+W) = 3136
+***********************************************************
+Assembly took 0.185992s.
+Preconditioner took 0.0221916s.
+   Pass :  1   Iteration :   0  ||B r|| = 41.2501
+   Pass :  1   Iteration :   1  ||B r|| = 41.2501
+   Pass :  1   Iteration :   2  ||B r|| = 0.000174926
+   Pass :  1   Iteration :   3  ||B r|| = 4.73276e-05
+   Pass :  1   Iteration :   4  ||B r|| = 5.87823e-06
+GMRES+UMFPack converged in 4 iterations with a residual norm of 5.87823e-06.
+GMRES solver took 0.0108975s.
+|| q_h - q_ex || / || q_ex || = 3.02391e-07
+|| t_h - t_ex || / || t_ex || = 1.63476e-07
@@ -0,0 +1,126 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 0
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --no-broken-RT
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --no-bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 0
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00686143s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.0120627s.
+Preconditioner took 7.2073e-05s.
+LBFGS iteration 0 : ||r|| = 0.0487525
+LBFGS iteration 1 : ||r|| = 0.0692476, ||r||/||r_0|| = 1.42039
+LBFGS iteration 2 : ||r|| = 0.0822451, ||r||/||r_0|| = 1.68699
+LBFGS iteration 3 : ||r|| = 0.118638, ||r||/||r_0|| = 2.43348
+LBFGS iteration 4 : ||r|| = 0.10805, ||r||/||r_0|| = 2.2163
+LBFGS iteration 5 : ||r|| = 0.123018, ||r||/||r_0|| = 2.52331
+LBFGS iteration 6 : ||r|| = 0.0331166, ||r||/||r_0|| = 0.67928
+LBFGS iteration 7 : ||r|| = 0.028239, ||r||/||r_0|| = 0.579233
+LBFGS iteration 8 : ||r|| = 0.0339501, ||r||/||r_0|| = 0.696376
+LBFGS iteration 9 : ||r|| = 0.0632489, ||r||/||r_0|| = 1.29735
+LBFGS iteration 10 : ||r|| = 0.0197064, ||r||/||r_0|| = 0.404214
+LBFGS iteration 11 : ||r|| = 0.0115797, ||r||/||r_0|| = 0.23752
+LBFGS iteration 12 : ||r|| = 0.0132388, ||r||/||r_0|| = 0.271551
+LBFGS iteration 13 : ||r|| = 0.0185307, ||r||/||r_0|| = 0.380097
+LBFGS iteration 14 : ||r|| = 0.0080584, ||r||/||r_0|| = 0.165292
+LBFGS iteration 15 : ||r|| = 0.0039921, ||r||/||r_0|| = 0.0818851
+LBFGS iteration 16 : ||r|| = 0.00336111, ||r||/||r_0|| = 0.0689424
+LBFGS iteration 17 : ||r|| = 0.00385752, ||r||/||r_0|| = 0.0791246
+LBFGS iteration 18 : ||r|| = 0.00192135, ||r||/||r_0|| = 0.0394103
+LBFGS iteration 19 : ||r|| = 0.000721511, ||r||/||r_0|| = 0.0147995
+LBFGS iteration 20 : ||r|| = 0.000602175, ||r||/||r_0|| = 0.0123517
+LBFGS iteration 21 : ||r|| = 0.000652919, ||r||/||r_0|| = 0.0133925
+LBFGS iteration 22 : ||r|| = 0.00115966, ||r||/||r_0|| = 0.0237866
+LBFGS iteration 23 : ||r|| = 0.000458624, ||r||/||r_0|| = 0.00940719
+LBFGS iteration 24 : ||r|| = 0.000389708, ||r||/||r_0|| = 0.0079936
+LBFGS iteration 25 : ||r|| = 0.000556569, ||r||/||r_0|| = 0.0114162
+LBFGS iteration 26 : ||r|| = 0.000629825, ||r||/||r_0|| = 0.0129188
+LBFGS iteration 27 : ||r|| = 0.00235984, ||r||/||r_0|| = 0.0484044
+LBFGS iteration 28 : ||r|| = 0.000319451, ||r||/||r_0|| = 0.00655251
+LBFGS iteration 29 : ||r|| = 0.000182618, ||r||/||r_0|| = 0.00374581
+LBFGS iteration 30 : ||r|| = 0.000134455, ||r||/||r_0|| = 0.00275791
+LBFGS iteration 31 : ||r|| = 0.000165894, ||r||/||r_0|| = 0.00340278
+LBFGS iteration 32 : ||r|| = 0.000266006, ||r||/||r_0|| = 0.00545626
+LBFGS iteration 33 : ||r|| = 0.000247654, ||r||/||r_0|| = 0.00507981
+LBFGS iteration 34 : ||r|| = 8.2696e-05, ||r||/||r_0|| = 0.00169624
+LBFGS iteration 35 : ||r|| = 6.20613e-05, ||r||/||r_0|| = 0.00127299
+LBFGS iteration 36 : ||r|| = 7.09828e-05, ||r||/||r_0|| = 0.00145598
+LBFGS iteration 37 : ||r|| = 0.000188153, ||r||/||r_0|| = 0.00385936
+LBFGS iteration 38 : ||r|| = 7.43305e-05, ||r||/||r_0|| = 0.00152465
+LBFGS iteration 39 : ||r|| = 5.84411e-05, ||r||/||r_0|| = 0.00119873
+LBFGS iteration 40 : ||r|| = 6.66851e-05, ||r||/||r_0|| = 0.00136783
+LBFGS iteration 41 : ||r|| = 8.73801e-05, ||r||/||r_0|| = 0.00179232
+LBFGS iteration 42 : ||r|| = 5.69932e-05, ||r||/||r_0|| = 0.00116903
+LBFGS iteration 43 : ||r|| = 1.66973e-05, ||r||/||r_0|| = 0.000342492
+LBFGS iteration 44 : ||r|| = 1.28376e-05, ||r||/||r_0|| = 0.000263322
+LBFGS iteration 45 : ||r|| = 1.44508e-05, ||r||/||r_0|| = 0.000296411
+LBFGS iteration 46 : ||r|| = 2.93946e-05, ||r||/||r_0|| = 0.000602936
+LBFGS iteration 47 : ||r|| = 6.07783e-06, ||r||/||r_0|| = 0.000124667
+LBFGS iteration 48 : ||r|| = 4.09353e-06, ||r||/||r_0|| = 8.39656e-05
+LBFGS iteration 49 : ||r|| = 4.37315e-06, ||r||/||r_0|| = 8.9701e-05
+LBFGS iteration 50 : ||r|| = 5.92802e-06, ||r||/||r_0|| = 0.000121594
+LBFGS iteration 51 : ||r|| = 6.92108e-06, ||r||/||r_0|| = 0.000141964
+LBFGS iteration 52 : ||r|| = 2.81197e-06, ||r||/||r_0|| = 5.76786e-05
+LBFGS iteration 53 : ||r|| = 2.16963e-06, ||r||/||r_0|| = 4.4503e-05
+LBFGS iteration 54 : ||r|| = 2.09303e-06, ||r||/||r_0|| = 4.29317e-05
+LBFGS iteration 55 : ||r|| = 3.14986e-06, ||r||/||r_0|| = 6.46092e-05
+LBFGS iteration 56 : ||r|| = 1.71347e-06, ||r||/||r_0|| = 3.51464e-05
+LBFGS iteration 57 : ||r|| = 1.61416e-06, ||r||/||r_0|| = 3.31093e-05
+LBFGS iteration 58 : ||r|| = 1.84854e-06, ||r||/||r_0|| = 3.79169e-05
+LBFGS iteration 59 : ||r|| = 4.36115e-06, ||r||/||r_0|| = 8.9455e-05
+LBFGS iteration 60 : ||r|| = 8.47721e-07, ||r||/||r_0|| = 1.73883e-05
+LBFGS iteration 61 : ||r|| = 4.73673e-07, ||r||/||r_0|| = 9.71588e-06
+LBFGS iteration 62 : ||r|| = 5.08728e-07, ||r||/||r_0|| = 1.04349e-05
+LBFGS iteration 63 : ||r|| = 5.89533e-07, ||r||/||r_0|| = 1.20924e-05
+LBFGS iteration 64 : ||r|| = 9.02349e-07, ||r||/||r_0|| = 1.85088e-05
+LBFGS iteration 65 : ||r|| = 2.67276e-07, ||r||/||r_0|| = 5.48231e-06
+LBFGS iteration 66 : ||r|| = 1.73874e-07, ||r||/||r_0|| = 3.56647e-06
+LBFGS iteration 67 : ||r|| = 1.67946e-07, ||r||/||r_0|| = 3.44488e-06
+LBFGS iteration 68 : ||r|| = 2.39486e-07, ||r||/||r_0|| = 4.91227e-06
+LBFGS iteration 69 : ||r|| = 1.74799e-07, ||r||/||r_0|| = 3.58544e-06
+LBFGS iteration 70 : ||r|| = 1.38108e-07, ||r||/||r_0|| = 2.83284e-06
+LBFGS iteration 71 : ||r|| = 1.5727e-07, ||r||/||r_0|| = 3.22588e-06
+LBFGS iteration 72 : ||r|| = 1.69831e-07, ||r||/||r_0|| = 3.48354e-06
+LBFGS iteration 73 : ||r|| = 1.44929e-07, ||r||/||r_0|| = 2.97275e-06
+LBFGS iteration 74 : ||r|| = 9.706e-08, ||r||/||r_0|| = 1.99087e-06
+LBFGS iteration 75 : ||r|| = 9.15601e-08, ||r||/||r_0|| = 1.87806e-06
+LBFGS iteration 76 : ||r|| = 1.55269e-07, ||r||/||r_0|| = 3.18485e-06
+LBFGS iteration 77 : ||r|| = 7.85595e-08, ||r||/||r_0|| = 1.6114e-06
+LBFGS iteration 78 : ||r|| = 3.44741e-08, ||r||/||r_0|| = 7.07125e-07
+LBFGS/Newton+GMRES converged in 78 iterations with a residual norm of 3.44741e-08.
+solver took 10.3609s.
+|| q_h - q_ex || / || q_ex || = 0.000103258
+|| t_h - t_ex || / || t_ex || = 6.13896e-05
@@ -0,0 +1,86 @@
+Options used:
+   --mesh 
+   --ncells-x 10
+   --ncells-y 10
+   --size-x 1
+   --size-y 1
+   --order 2
+   --discontinuous
+   --centered
+   --problem 2
+   --time-final 1
+   --ntimesteps 0
+   --ode-solver 1
+   --kappa 1
+   --velocity 1
+   --stab_diff 0.5
+   --bc-neumann
+   --no-reduction
+   --hybridization
+   --nonlinear
+   --no-nonlinear-convection
+   --no-nonlinear-diffusion
+   --hdg_scheme 1
+   --nonlinear-solver 3
+   --no-partial-assembly
+   --device cpu
+   --no-mfem
+   --no-visit
+   --no-paraview
+   --no-visualization
+   --no-analytic
+Device configuration: cpu
+Memory configuration: host-std
+Hybridization init took 0.00638558s.
+***********************************************************
+dim(V) = 1800
+dim(W) = 900
+dim(M) = 660
+dim(V+W+M) = 3360
+***********************************************************
+Assembly took 0.00964168s.
+Preconditioner took 3.6389e-05s.
+Newton iteration  0 : ||r|| = 0.102997
+Newton iteration  1 : ||r|| = 0.000212358, ||r||/||r_0|| = 0.00206179
+Newton iteration  2 : ||r|| = 7.28894e-05, ||r||/||r_0|| = 0.000707684
+Newton iteration  3 : ||r|| = 3.17779e-05, ||r||/||r_0|| = 0.000308532
+Newton iteration  4 : ||r|| = 2.76903e-05, ||r||/||r_0|| = 0.000268845
+Newton iteration  5 : ||r|| = 2.17462e-05, ||r||/||r_0|| = 0.000211134
+Newton iteration  6 : ||r|| = 1.7992e-05, ||r||/||r_0|| = 0.000174684
+Newton iteration  7 : ||r|| = 1.50151e-05, ||r||/||r_0|| = 0.000145781
+Newton iteration  8 : ||r|| = 1.26765e-05, ||r||/||r_0|| = 0.000123076
+Newton iteration  9 : ||r|| = 1.07699e-05, ||r||/||r_0|| = 0.000104565
+Newton iteration 10 : ||r|| = 9.18746e-06, ||r||/||r_0|| = 8.92011e-05
+Newton iteration 11 : ||r|| = 7.85578e-06, ||r||/||r_0|| = 7.62718e-05
+Newton iteration 12 : ||r|| = 6.72573e-06, ||r||/||r_0|| = 6.53002e-05
+Newton iteration 13 : ||r|| = 5.76189e-06, ||r||/||r_0|| = 5.59422e-05
+Newton iteration 14 : ||r|| = 4.93744e-06, ||r||/||r_0|| = 4.79377e-05
+Newton iteration 15 : ||r|| = 4.23115e-06, ||r||/||r_0|| = 4.10802e-05
+Newton iteration 16 : ||r|| = 3.62564e-06, ||r||/||r_0|| = 3.52014e-05
+Newton iteration 17 : ||r|| = 3.10642e-06, ||r||/||r_0|| = 3.01602e-05
+Newton iteration 18 : ||r|| = 2.66118e-06, ||r||/||r_0|| = 2.58375e-05
+Newton iteration 19 : ||r|| = 2.27945e-06, ||r||/||r_0|| = 2.21312e-05
+Newton iteration 20 : ||r|| = 1.95223e-06, ||r||/||r_0|| = 1.89543e-05
+Newton iteration 21 : ||r|| = 1.6718e-06, ||r||/||r_0|| = 1.62315e-05
+Newton iteration 22 : ||r|| = 1.43151e-06, ||r||/||r_0|| = 1.38985e-05
+Newton iteration 23 : ||r|| = 1.22566e-06, ||r||/||r_0|| = 1.18999e-05
+Newton iteration 24 : ||r|| = 1.04934e-06, ||r||/||r_0|| = 1.0188e-05
+Newton iteration 25 : ||r|| = 8.98328e-07, ||r||/||r_0|| = 8.72188e-06
+Newton iteration 26 : ||r|| = 7.69016e-07, ||r||/||r_0|| = 7.46639e-06
+Newton iteration 27 : ||r|| = 6.58293e-07, ||r||/||r_0|| = 6.39137e-06
+Newton iteration 28 : ||r|| = 5.63494e-07, ||r||/||r_0|| = 5.47097e-06
+Newton iteration 29 : ||r|| = 4.82335e-07, ||r||/||r_0|| = 4.68299e-06
+Newton iteration 30 : ||r|| = 4.12856e-07, ||r||/||r_0|| = 4.00842e-06
+Newton iteration 31 : ||r|| = 3.5338e-07, ||r||/||r_0|| = 3.43096e-06
+Newton iteration 32 : ||r|| = 3.02467e-07, ||r||/||r_0|| = 2.93666e-06
+Newton iteration 33 : ||r|| = 2.58889e-07, ||r||/||r_0|| = 2.51355e-06
+Newton iteration 34 : ||r|| = 2.21585e-07, ||r||/||r_0|| = 2.15137e-06
+Newton iteration 35 : ||r|| = 1.89656e-07, ||r||/||r_0|| = 1.84137e-06
+Newton iteration 36 : ||r|| = 1.62327e-07, ||r||/||r_0|| = 1.57603e-06
+Newton iteration 37 : ||r|| = 1.38934e-07, ||r||/||r_0|| = 1.34891e-06
+Newton iteration 38 : ||r|| = 1.18913e-07, ||r||/||r_0|| = 1.15453e-06
+Newton iteration 39 : ||r|| = 1.01775e-07, ||r||/||r_0|| = 9.88139e-07
+Newton+GMRES+GS/Newton+GMRES converged in 39 iterations with a residual norm of 1.01775e-07.
+solver took 13.3521s.
+|| q_h - q_ex || / || q_ex || = 0.000108111
+|| t_h - t_ex || / || t_ex || = 1.8685e-05
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+++ b/Show More