adding the missing makefile and updating some of the files, cleanup, etc

simple interior-point solver code with generic problem structure and a few example problems
Merge pull request #4123 from mfem/najlkin/mixed-DG
2024-10-16 10:30:28 -07:00 · 2024-10-15 17:20:18 -07:00 · 2024-10-14 18:03:19 -07:00 · 2024-10-04 15:52:48 -07:00 · 2024-10-01 13:15:15 -07:00 · 2024-10-01 13:10:28 -07:00
406 changed files with 17906 additions and 66923 deletions
@@ -0,0 +1,31 @@
+# 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.
+
+name: "Trigger PyMFEM CI"
+
+on:
+  push:
+    branches:
+      - master
+
+jobs:
+  trigger-pymfem:
+    runs-on: ubuntu-latest
+    steps:
+    - name: Send POST request to trigger PyMFEM CI
+      run: |
+        curl -L \
+             -X POST \
+             -H "Accept: application/vnd.github+json" \
+             -H "Authorization: Bearer ${{ secrets.PYMFEM_CI_TOKEN }}" \
+             -H "X-GitHub-Api-Version: 2022-11-28" \
+             https://api.github.com/repos/mfem/pymfem/actions/workflows/build-and-test-dispatch.yml/dispatches \
+             -d '{"ref":"master", "inputs":{"test_options":"fast"}}'
@@ -15,6 +15,9 @@
 CMakeCache.txt
 CMakeFiles/

+# Clangd server cache
+*.cache*
+
 # Backup files
 *~

@@ -272,16 +275,27 @@ miniapps/navier/*_output

 miniapps/nurbs/nurbs_ex1
 miniapps/nurbs/nurbs_ex1p
+miniapps/nurbs/nurbs_ex3
+miniapps/nurbs/nurbs_ex5
 miniapps/nurbs/nurbs_ex11p
+miniapps/nurbs/nurbs_ex24
+miniapps/nurbs/nurbs_solenoidal
 miniapps/nurbs/nurbs_printfunc
 miniapps/nurbs/nurbs_patch_ex1
 miniapps/nurbs/nurbs_curveint
 miniapps/nurbs/refined.mesh
 miniapps/nurbs/mesh.*
+miniapps/nurbs/sol_?.gf
 miniapps/nurbs/sol.*
 miniapps/nurbs/mode_*
 miniapps/nurbs/Example1*
+miniapps/nurbs/Example3*
+miniapps/nurbs/Example5*
+miniapps/nurbs/Solenoidal*
+miniapps/nurbs/ParaView
 miniapps/nurbs/sin-fit.mesh
+miniapps/nurbs/ex5.mesh
+miniapps/nurbs/exsol.mesh
 miniapps/nurbs/CurveInt
 miniapps/nurbs/nurbs_naca_cmesh
 miniapps/nurbs/naca-cmesh.mesh
@@ -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 quartz 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:
-quartz-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 @@ quartz-build-and-test:
    AUTOTEST: "${AUTOTEST}"
    AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
  trigger:
-    include: .gitlab/quartz-build-and-test.yml
+    include: .gitlab/ruby-build-and-test.yml
    strategy: depend

-quartz-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 @@ quartz-baseline:
    AUTOTEST: "${AUTOTEST}"
    AUTOTEST_COMMIT: "${AUTOTEST_COMMIT}"
  trigger:
-    include: .gitlab/quartz-baseline.yml
+    include: .gitlab/ruby-baseline.yml
    strategy: depend

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

 Machines typically include:

-* Quartz: Intel bi-socket x86
+* 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 quartz 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_quartz
+  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 quartz, 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 Quartz machine at LLNL
+# GitLab pipelines configurations for the Ruby machine at LLNL
 variables:
-  MACHINE_NAME: quartz
+  MACHINE_NAME: ruby

-.on_quartz:
+.on_ruby:
  tags:
    - shell
-    - quartz
+    - ruby
  rules:
-    # Don't run quartz jobs if...
-    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_QUARTZ == "OFF"'
+    # Don't run ruby jobs if...
+    - if: '$CI_COMMIT_BRANCH =~ /_qnone/ || $ON_RUBY == "OFF"'
      when: never
    # Don't run autotest update if...
    - if: '$CI_JOB_NAME =~ /report/ && $AUTOTEST != "YES"'
@@ -40,13 +40,13 @@ variables:
    - when: on_success

 # Spack helped builds
-# Generic quartz build job, extending build script
-.build_and_test_on_quartz:
-  extends: [.on_quartz]
+# 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
-    - export THREADS=12
+    - export THREADS=16
    - echo ${ALLOC_NAME}
    - export JOBID=$(squeue -h --name=${ALLOC_NAME} --format=%A)
    - echo ${JOBID}
@@ -18,7 +18,7 @@
 setup_baseline:
  tags:
    - shell
-    - quartz
+    - ruby
  stage: setup
  variables:
    GIT_STRATEGY: none
@@ -16,7 +16,7 @@
 setup:
  tags:
    - shell
-    - quartz
+    - ruby
  stage: setup
  variables:
    GIT_STRATEGY: none
@@ -19,8 +19,8 @@ stages:
  - cleanup
  - baseline_publish

-baselinecheck_mfem_intel_quartz:
-  extends: [.on_quartz]
+baselinecheck_mfem_intel_ruby:
+  extends: [.on_ruby]
  stage: baseline_check
  variables:
    # TPLS_DIR is used in .gitlab/scripts/baseline to provide the tpls location
@@ -32,7 +32,7 @@ baselinecheck_mfem_intel_quartz:
    - echo ${BUILD_ROOT}
    - echo ${TPLS_DIR}
    # Used by the tests in MFEM/tests:
-    - export MFEM_TEST_NP=32
+    - 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
@@ -44,18 +44,16 @@ baselinecheck_mfem_intel_quartz:
  allow_failure: true

 cleanup:
-  extends: .on_quartz
+  extends: .on_ruby
  stage: cleanup
  variables:
    GIT_STRATEGY: none
  script:
    - echo "BUILD_ROOT=${BUILD_ROOT}"
    - rm -rf "${BUILD_ROOT}" || true
-    - echo "CI_PROJECT_DIR=${CI_PROJECT_DIR}"
-    - make -C "${CI_PROJECT_DIR}" distclean

 report_baseline:
-  extends: [.on_quartz]
+  extends: [.on_ruby]
  stage: baseline_report
  script:
    - echo ${MACHINE_NAME}
@@ -115,8 +113,8 @@ report_baseline:
        exit $err
      ) 9> autotest.lock

-baselinepublish_mfem_quartz:
-  extends: [.on_quartz]
+baselinepublish_mfem_ruby:
+  extends: [.on_ruby]
  stage: baseline_publish
  rules:
    # - if: '$CI_COMMIT_BRANCH == "master" || $REBASELINE == "YES"'
@@ -131,5 +129,5 @@ baselinepublish_mfem_quartz:

 include:
  - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-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_quartz
+  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 Quartz 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_quartz
+  extends: .build_and_test_on_ruby

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

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

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

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

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

 # Release
 release_resource:
  variables:
    GIT_STRATEGY: none
-  extends: .on_quartz
+  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_quartz
+    - .on_ruby
    - .report_job_success

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

 include:
  - local: .gitlab/configs/common.yml
-  - local: .gitlab/configs/quartz-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}" == "quartz" ]]; then
+if [[ "${MACHINE_NAME}" == "ruby" ]]; then
  base="${BASELINE_TEST}-${MACHINE_NAME}"
 fi
 base_diff=${base}.diff
@@ -31,8 +31,8 @@ cd tests
 mkdir _${BASELINE_TEST} && cd _${BASELINE_TEST}

 # run
-if [[ "${MACHINE_NAME}" == "quartz" || "${MACHINE_NAME}" == "ruby" ]]; then
-  salloc --nodes=1 --reservation=ci ../runtest ../../mfem "${BASELINE_TEST} ${TPLS_DIR}"
+if [[ "${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}"
 elif [[ ${MACHINE_NAME} == "lassen" ]]; then
@@ -41,11 +41,11 @@ else
  echo "Unknown machine: MACHINE_NAME=$MACHINE_NAME"
  exit 1
 fi
+status="$?"

 # post
 mkdir ${artifacts_path}

-status=0
 if [[ -f ${BASELINE_TEST}.out ]]; then
  cp ${BASELINE_TEST}.out ${artifacts_path}
 fi
@@ -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 quartz 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 quartz 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
@@ -11,9 +11,63 @@
 Version 4.7.1 (development)
 ===========================

+Discretization improvements
+---------------------------
+- Added NURBS-based H(div) and H(curl) elements in 2D and 3D. Only on single
+  patch meshes. Only implemented for serial computations.
+
+- Added support for boundary constraints to the hybridization class.
+
+Meshing improvements
+--------------------
+- The ExodusII reader now handles pyramid and wedge element types. Mixed meshes
+  are also supported.
+
+New and updated examples and miniapps
+-------------------------------------
+- Added miniapps to demonstrate the H(div) and H(curl) NURBS elements.
+
 - Added an MFEM example for the eikonal equation. This new solver is based on
  the proximal Galerkin method introduced by Keith and Surowiec.

+- Added a command line option to all miniapps (`-p` or `--send-port`) for
+  specifying the GLVis server socket port (19916 by default).
+
+GPU computing
+-------------
+- Added support for GPU-accelerated batched linear algebra (using cuBLAS,
+  hipBLAS, MAGMA, or native MFEM functionality) through the BatchedLinAlg class.
+
+- A new GPU kernel dispatch mechanism was introduced. Users can instantiate
+  specialized kernels for specific combinations of (for example) polynomial
+  degree and number of quadrature points using
+  `DiffusionIntegrator::AddSpecialization` and
+  `MassIntegrator::AddSpecialization` (this functionality may be added to more
+  integrators in the future).
+
+- Calls to slower fallback kernels can be reported to `mfem::err` by setting
+  the environment variable `MFEM_REPORT_KERNELS` to any value other than `NO`
+  or by explicitly calling `KernelReporter::Enable`. Users can then add
+  specializations for these kernels to achieve higher performance.
+
+Miscellaneous
+-------------
+- Refactored the `ARKStepSolver` class (ARKODE interface) to use
+  `TimeDependentOperator::Mult` only when the associated ODE operator is
+  expressed in explicit form (i.e., `TimeDependentOperator::isExplicit()`),
+  otherwise `TimeDependentOperator::ExplicitMult` is used. A check has been
+  added to `ARKStepSolver` to verify that the associated ODE operator is not in
+  explicit form when a mass matrix solver is enabled via a call to either the
+  `UseMFEMMassLinearSolver` or `UseSundialsMassLinearSolver` methods. This is
+  because enabling a mass matrix solver assumes that F(u,k,t) = M k in the
+  associated ODE operator.
+
+- Added support for custom interpolation procedure in FindPointsGSLIB.
+
+API changes
+-----------
+- API change: in class GridFunction, 'fec' was renamed to 'fec_owned'.
+

 Version 4.7, released on May 7, 2024
 ====================================
@@ -38,6 +92,9 @@ Meshing improvements

 - Added support for internal boundary elements in nonconforming meshes.

+- Added ExodusII output capability. The writer can handle first-order (Pyramid5,
+  Wedge6, Hex8, Tet4) and second-order FE types (Pyramid14, Wedge18, Hex27, Tet10).
+
 - The ReadCubit Genesis mesh importer has been rewritten to improve readability.

 Discretization improvements
@@ -146,7 +146,9 @@ if (MFEM_USE_CUDA)
   set(CMAKE_CUDA_FLAGS "${CMAKE_CUDA_FLAGS} ${CUDA_FLAGS}")
   find_package(CUDAToolkit REQUIRED)
   set(CUSPARSE_FOUND TRUE)
+   set(CUBLAS_FOUND TRUE)
   get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
+   get_target_property(CUBLAS_LIBRARIES CUDA::cublas LOCATION)
 endif()

 if (XSDK_ENABLE_C)
@@ -231,6 +233,7 @@ if (MFEM_USE_HIP)
    list(INSERT CMAKE_PREFIX_PATH 0 ${ROCM_PATH})
  endif()
  find_package(HIP REQUIRED)
+  find_package(HIPBLAS REQUIRED)
  find_package(HIPSPARSE REQUIRED)
 endif()

@@ -396,6 +399,10 @@ if (MFEM_USE_AMGX)
  find_package(AMGX REQUIRED)
 endif()

+if (MFEM_USE_MAGMA)
+  find_package(MAGMA REQUIRED)
+endif()
+
 if (MFEM_USE_CONDUIT)
    find_package(Conduit REQUIRED conduit relay blueprint)
 endif()
@@ -557,8 +564,9 @@ find_package(Threads REQUIRED)
 set(MFEM_TPLS OPENMP HYPRE LAPACK BLAS SuperLUDist STRUMPACK METIS SuiteSparse
    SUNDIALS PETSC SLEPC MUMPS AXOM FMS CONDUIT Ginkgo GNUTLS GSLIB
    NETCDF MPFR PUMI HIOP POSIXCLOCKS MFEMBacktrace ZLIB OCCA CEED RAJA UMPIRE
-    ADIOS2 CUSPARSE MKL_CPARDISO MKL_PARDISO AMGX CALIPER CODIPACK
-    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPSPARSE MOONOLITH BLITZ ALGOIM ENZYME)
+    ADIOS2 MKL_CPARDISO MKL_PARDISO AMGX MAGMA CUSPARSE CUBLAS CALIPER CODIPACK
+    BENCHMARK PARELAG TRIBOL MPI_CXX HIP HIPBLAS HIPSPARSE MOONOLITH BLITZ
+    ALGOIM ENZYME)

 # Add all *_FOUND libraries in the variable TPL_LIBRARIES.
 set(TPL_LIBRARIES "")
@@ -673,7 +681,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
 #include \"${PROJECT_SOURCE_DIR}/${Header}\"
 ")

-    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different
      "${PROJECT_BINARY_DIR}/${Header}.tmp"
      "${PROJECT_BINARY_DIR}/${Header}"
    )
@@ -687,7 +695,7 @@ if (NOT ("${PROJECT_SOURCE_DIR}" STREQUAL "${PROJECT_BINARY_DIR}"))
 #include \"mfem/${Header}\"
 ")

-    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different 
+    execute_process(COMMAND ${CMAKE_COMMAND} -E copy_if_different
      "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}.tmp"
      "${PROJECT_BINARY_DIR}/InstallHeaders/${Header}"
    )
@@ -273,7 +273,13 @@ Installation options:
   PREFIX  - Specify the installation directory. The library (libmfem.a) will be
             installed in $(PREFIX)/lib, the headers in $(PREFIX)/include, and
             the configuration makefile (config.mk) in $(PREFIX)/share/mfem.
-   INSTALL - Specify the install program, e.g /usr/bin/install
+   INSTALL - Specify the install program, default = /usr/bin/install
+   INSTALL_DEF_PERM - Specify the default install permissions. This affects
+                      headers and configuration makefiles, default = 644
+   INSTALL_BIN_PERM - Specify the install permissions for binaries. This only
+                      affects the shared version of the library, default = 755
+   INSTALL_DIR_PERM - Specify the install permissions for directories and,
+                      on macOS/BSD, for symlinks as well, default = 755

 MFEM library features/options (GNU make)
 ----------------------------------------
@@ -388,6 +394,11 @@ MFEM_USE_AMGX = YES/NO
   Allows the user to use SparseMatrices and HypreParMatrices to solve linear
   systems with the routines from the AmgX library.

+MFEM_USE_MAGMA = YES/NO
+   Enable MFEM functionality based on the MAGMA high-performance linear algebra
+   library. The MAGMA library provides a BLAS/LAPACK interface, with
+   implementations that have been optimized for Nvidia and AMD GPUs.
+
 MFEM_USE_GNUTLS = YES/NO
   Enable secure socket support in class socketstream, using the auxiliary
   GnuTLS_* classes, based on the GnuTLS library. This option may be useful in
@@ -699,6 +710,11 @@ The specific libraries and their options are:
  Options: AMGX_OPT, AMGX_LIB.
  Versions: AmgX >= 2.1, older versions may work too.

+- MAGMA (optional), used with MFEM_USE_MAGMA = YES.
+  URL: https://icl.utk.edu/magma/
+  Options: MAGMA_OPT, MAGMA_LIB
+  Versions: MAGMA >= 2.8.0
+
 - GnuTLS (optional), used when MFEM_USE_GNUTLS = YES. On most Linux systems,
  GnuTLS is available as a development package, e.g. gnutls-devel. On Mac OS X,
  one can get the library through the Homebrew package manager (http://brew.sh).
@@ -37,6 +37,7 @@ set(MFEM_USE_MUMPS @MFEM_USE_MUMPS@)
 set(MFEM_USE_STRUMPACK @MFEM_USE_STRUMPACK@)
 set(MFEM_USE_GINKGO @MFEM_USE_GINKGO@)
 set(MFEM_USE_AMGX @MFEM_USE_AMGX@)
+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@)
@@ -114,6 +114,9 @@
 // Enable MFEM functionality based on the AmgX library.
 #cmakedefine MFEM_USE_AMGX

+// Enable MFEM functionality based on the MAGMA library.
+#cmakedefine MFEM_USE_MAGMA
+
 // Enable secure socket streams based on the GNUTLS library.
 #cmakedefine MFEM_USE_GNUTLS

@@ -0,0 +1,37 @@
+# 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.
+
+# Defines the following variables:
+#   - MAGMA_FOUND
+#   - MAGMA_LIBRARIES
+#   - MAGMA_INCLUDE_DIRS
+
+include(MfemCmakeUtilities)
+mfem_find_package(MAGMA MAGMA MAGMA_DIR "include" "magma.h" "lib" "magma"
+  "Paths to headers required by MAGMA." "Libraries required by MAGMA.")
+
+if (MAGMA_FOUND AND MFEM_USE_CUDA)
+  get_target_property(CUSPARSE_LIBRARIES CUDA::cusparse LOCATION)
+  get_target_property(CUBLAS_LIBRARIES CUDA::cublas LOCATION)
+  list(APPEND MAGMA_LIBRARIES ${CUSPARSE_LIBRARIES} ${CUBLAS_LIBRARIES})
+  set(MAGMA_LIBRARIES ${MAGMA_LIBRARIES} CACHE STRING
+      "MAGMA libraries + dependencies." FORCE)
+  message(STATUS "Updated MAGMA_LIBRARIES: ${MAGMA_LIBRARIES}")
+endif()
+
+if (MAGMA_FOUND AND MFEM_USE_HIP)
+  find_package(HIPBLAS REQUIRED)
+  find_package(HIPSPARSE REQUIRED)
+  list(APPEND MAGMA_LIBRARIES ${HIPBLAS_LIBRARIES} ${HIPSPARSE_LIBRARIES})
+  set(MAGMA_LIBRARIES ${MAGMA_LIBRARIES} CACHE STRING
+      "MAGMA libraries + dependencies." FORCE)
+  message(STATUS "Updated MAGMA_LIBRARIES: ${MAGMA_LIBRARIES}")
+endif()
@@ -846,14 +846,14 @@ function(mfem_export_mk_files)
      MFEM_USE_ZLIB MFEM_USE_LIBUNWIND MFEM_USE_LAPACK MFEM_THREAD_SAFE
      MFEM_USE_LEGACY_OPENMP MFEM_USE_OPENMP MFEM_USE_MEMALLOC MFEM_USE_SUNDIALS
      MFEM_USE_SUITESPARSE MFEM_USE_SUPERLU MFEM_USE_SUPERLU5 MFEM_USE_MUMPS
-      MFEM_USE_STRUMPACK MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_GNUTLS
-      MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_SLEPC MFEM_USE_MPFR MFEM_USE_SIDRE
-      MFEM_USE_FMS MFEM_USE_CONDUIT MFEM_USE_PUMI MFEM_USE_HIOP MFEM_USE_GSLIB
-      MFEM_USE_CUDA MFEM_USE_HIP MFEM_USE_RAJA 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_STRUMPACK MFEM_USE_GINKGO MFEM_USE_AMGX MFEM_USE_MAGMA
+      MFEM_USE_GNUTLS MFEM_USE_NETCDF MFEM_USE_PETSC MFEM_USE_SLEPC
+      MFEM_USE_MPFR MFEM_USE_SIDRE MFEM_USE_FMS MFEM_USE_CONDUIT MFEM_USE_PUMI
+      MFEM_USE_HIOP MFEM_USE_GSLIB MFEM_USE_CUDA MFEM_USE_HIP MFEM_USE_RAJA
+      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)
  foreach(var ${CONFIG_MK_BOOL_VARS})
    if (${var})
      set(${var} YES)
@@ -114,6 +114,9 @@
 // Enable MFEM functionality based on the AmgX library.
 // #define MFEM_USE_AMGX

+// Enable MFEM functionality based on the MAGMA library.
+// #define MFEM_USE_MAGMA
+
 // Enable secure socket streams based on the GNUTLS library.
 // #define MFEM_USE_GNUTLS

@@ -38,6 +38,7 @@ MFEM_USE_MUMPS         = @MFEM_USE_MUMPS@
 MFEM_USE_STRUMPACK     = @MFEM_USE_STRUMPACK@
 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_NETCDF        = @MFEM_USE_NETCDF@
 MFEM_USE_PETSC         = @MFEM_USE_PETSC@
@@ -40,6 +40,7 @@ option(MFEM_USE_MUMPS "Enable MUMPS usage" OFF)
 option(MFEM_USE_STRUMPACK "Enable STRUMPACK usage" OFF)
 option(MFEM_USE_GINKGO "Enable Ginkgo usage" OFF)
 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_NETCDF "Enable NETCDF usage" OFF)
@@ -183,6 +184,10 @@ set(Ginkgo_DIR "${MFEM_DIR}/../ginkgo" CACHE PATH "Path to the Ginkgo library.")

 set(AMGX_DIR "${MFEM_DIR}/../amgx" CACHE PATH "Path to AmgX")

+set(MAGMA_DIR "${MFEM_DIR}/../magma" CACHE PATH "Path to MAGMA")
+set(MAGMA_REQUIRED_PACKAGES "BLAS" "LAPACK" CACHE STRING
+    "Additional packages required by MAGMA.")
+
 set(GNUTLS_DIR "" CACHE PATH "Path to the GnuTLS library.")

 set(GSLIB_DIR "" CACHE PATH "Path to the GSLIB library.")
@@ -259,7 +264,7 @@ set(PARELAG_LIBRARIES "${PARELAG_DIR}/build/src/libParELAG.a" CACHE STRING
    "The ParELAG library.")

 set(TRIBOL_DIR "${MFEM_DIR}/../tribol" CACHE PATH "Path to Tribol")
-set(Tribol_REQUIRED_PACKAGES "Axom/core/mint/slam/slic" CACHE STRING 
+set(Tribol_REQUIRED_PACKAGES "Axom/core/mint/slam/slic" CACHE STRING
    "Additional packages required by Tribol")

 set(BLAS_INCLUDE_DIRS "" CACHE STRING "Path to BLAS headers.")
@@ -95,6 +95,10 @@ else
   # Silence unused command line argument warnings when generating dependencies
   # with mpicxx and clang
   DEP_FLAGS := -Wno-unused-command-line-argument $(DEP_FLAGS)
+   # Silence "ignoring duplicate libraries" warnings on new (Xcode 15) linker
+   ifneq (,$(findstring PROJECT:dyld,$(shell ld -v 2>&1)))
+      LDFLAGS_INTERNAL = -Xlinker -no_warn_duplicate_libraries
+   endif
 endif

 # Set CXXFLAGS to overwrite the default selection of DEBUG_FLAGS/OPTIM_FLAGS
@@ -139,6 +143,7 @@ MFEM_USE_MUMPS         = NO
 MFEM_USE_STRUMPACK     = NO
 MFEM_USE_GINKGO        = NO
 MFEM_USE_AMGX          = NO
+MFEM_USE_MAGMA         = NO
 MFEM_USE_GNUTLS        = NO
 MFEM_USE_NETCDF        = NO
 MFEM_USE_PETSC         = NO
@@ -390,6 +395,11 @@ AMGX_DIR = @MFEM_DIR@/../amgx
 AMGX_OPT = -I$(AMGX_DIR)/include
 AMGX_LIB = -L$(AMGX_DIR)/lib -lamgx -lcusparse -lcusolver -lcublas -lnvToolsExt

+# MAGMA library configuration
+MAGMA_DIR = @MFEM_DIR@/../magma
+MAGMA_OPT = -I$(MAGMA_DIR)/include
+MAGMA_LIB = -L$(MAGMA_DIR)/lib -l:libmagma.a -lcublas -lcusparse $(LAPACK_LIB)
+
 # GnuTLS library configuration
 GNUTLS_OPT =
 GNUTLS_LIB = -lgnutls
@@ -497,11 +507,11 @@ GSLIB_LIB = -L$(GSLIB_DIR)/lib -lgs

 # CUDA library configuration
 CUDA_OPT =
-CUDA_LIB = -lcusparse
+CUDA_LIB = -lcusparse -lcublas

 # HIP library configuration
 HIP_OPT =
-HIP_LIB = -L$(HIP_DIR)/lib $(XLINKER)-rpath,$(HIP_DIR)/lib -lhipsparse
+HIP_LIB = -L$(HIP_DIR)/lib $(XLINKER)-rpath,$(HIP_DIR)/lib -lhipsparse -lhipblas

 # OCCA library configuration
 OCCA_DIR = @MFEM_DIR@/../occa
@@ -32,7 +32,7 @@ groups_serial=(
 '"examples"
   "Examples:"
   "examples"
-   "ex{,1,2,3}[0-9].cpp"'
+   "ex{,[1-9]}[0-9].cpp"'
 #   "ex1.cpp"'
 '"sundials"
   "SUNDIALS examples:"
@@ -58,6 +58,10 @@ groups_serial=(
   "HiOp examples:"
   "examples/hiop"
   "ex9.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp"'
 '"pumi"
   "PUMI examples:"
   "examples/pumi"
@@ -66,25 +70,38 @@ groups_serial=(
 '"meshing"
   "Meshing miniapps:"
   "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
    mesh-optimizer.cpp minimal-surface.cpp"'
 '"adjoint"
   "Adjoint miniapps:"
   "miniapps/adjoint"
   "cvsRoberts_ASAi_dns.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp"' # 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
   "GSLIB miniapps:"
   "miniapps/gslib"
   "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp "'
+# todo: miniapps/mtop
 '"nurbs"
   "NURBS miniapps:"
   "miniapps/nurbs"
   "nurbs_ex1.cpp"'
+# todo: add other nurbs miniapps
+# todo: miniapps/solvers (serial)
 '"tools"
   "Tools miniapps:"
   "miniapps/tools"
   "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
    lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
   "Toys miniapps:"
   "miniapps/toys"
@@ -100,7 +117,7 @@ groups_parallel=(
 '"examples"
   "Examples:"
   "examples"
-   "ex{,1,2,3}[0-9]p.cpp"'
+   "ex{,[1-9]}[0-9]p.cpp"'
 #   "ex1p.cpp"'
 '"sundials"
   "SUNDIALS examples:"
@@ -126,6 +143,10 @@ groups_parallel=(
   "HiOp examples:"
   "examples/hiop"
   "ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex{1,2}p.cpp"'
 '"pumi"
   "PUMI examples:"
   "examples/pumi"
@@ -138,24 +159,41 @@ groups_parallel=(
 '"meshing"
   "Meshing miniapps:"
   "miniapps/meshing"
-   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp"'
+   "pmesh-optimizer.cpp pmesh-fitting.cpp pminimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
   "Electromagnetics miniapps:"
   "miniapps/electromagnetics"
   "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
   "Adjoint miniapps:"
   "miniapps/adjoint"
   "adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "par_example.cpp"'
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "p{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
   "GSLIB miniapps:"
   "miniapps/gslib"
   "pfindpts.cpp schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
   "Navier miniapps:"
   "miniapps/navier"
   "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
   "NURBS miniapps:"
   "miniapps/nurbs"
@@ -164,14 +202,18 @@ groups_parallel=(
   "Shifted miniapps:"
   "miniapps/shifted"
   "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
   "Solvers miniapps:"
   "miniapps/solvers"
   "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
   "Tools miniapps:"
   "miniapps/tools"
-   "convert-cd.cpp get-values.cpp load-dc.cpp"'
+   "convert-dc.cpp get-values.cpp load-dc.cpp"'
+# todo: add other tools miniapps
 '"convergence"
   "Convergence tests:"
   "tests/convergence"
@@ -186,7 +228,7 @@ groups_all=(
 '"examples"
   "Examples:"
   "examples"
-   "ex\"{,1,2,3}[0-9]\"{,p}.cpp"'
+   "ex\"{,[1-9]}[0-9]\"{,p}.cpp"'
 '"sundials"
   "SUNDIALS examples:"
   "examples/sundials"
@@ -215,10 +257,14 @@ groups_all=(
   "HiOp examples:"
   "examples/hiop"
   "ex9.cpp ex9p.cpp"'
+'"moonolith"
+   "Moonolith examples:"
+   "examples/moonolith"
+   "ex1.cpp ex{1,2}p.cpp"'
 '"pumi"
   "PUMI examples:"
   "examples/pumi"
-   "ex1.cpp ex1p.cpp ex2.cpp ex6p.cpp"'
+   "ex1.cpp ex2.cpp ex1p.cpp ex6p.cpp"'
 '"superlu"
   "Superlu examples:"
   "examples/superlu"
@@ -226,43 +272,67 @@ groups_all=(
 '"meshing"
   "Meshing miniapps:"
   "miniapps/meshing"
-   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp
-    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp"'
+   "mobius-strip.cpp klein-bottle.cpp extruder.cpp toroid.cpp mesh-quality.cpp
+    polar-nc.cpp reflector.cpp shaper.cpp trimmer.cpp twist.cpp
+    {,p}mesh-optimizer.cpp pmesh-fitting.cpp {,p}minimal-surface.cpp
+    fit-node-position.cpp"'
 '"electromagnetics"
   "Electromagnetics miniapps:"
   "miniapps/electromagnetics"
   "joule.cpp"'
-#   "{volta,tesla,joule}.cpp"' # todo: multiline sample runs
+#   "{joule,maxwell,tesla,volta}.cpp"' # todo: multiline sample runs
 '"adjoint"
   "Adjoint miniapps:"
   "miniapps/adjoint"
-   "adjoint_advection_diffusion.cpp cvsRoberts_ASAi_dns.cpp"'
+   "cvsRoberts_ASAi_dns.cpp adjoint_advection_diffusion.cpp"'
+'"autodiff"
+   "Autodiff miniapps:"
+   "miniapps/autodiff"
+   "seq_example.cpp seq_test.cpp par_example.cpp"'
+# 'seq_test.cpp' has no sample runs
+'"dpg"
+   "DPG miniapps:"
+   "miniapps/dpg"
+   "{,p}{acoustics,convection-diffusion,diffusion,maxwell}.cpp"'
 '"gslib"
   "GSLIB miniapps:"
   "miniapps/gslib"
   "field-diff.cpp field-interp.cpp findpts.cpp schwarz_ex1.cpp pfindpts.cpp
    schwarz_ex1p.cpp"'
+'"hdiv-linear-solver"
+   "H(div) linear solver miniapps:"
+   "miniapps/hdiv-linear-solver"
+   "grad_div.cpp darcy.cpp"'
+# 'miniapps/hooke/hooke.cpp' has no sample runs
+# todo: miniapps/mtop
+# todo: miniapps/multidomain
 '"navier"
   "Navier miniapps:"
   "miniapps/navier"
   "navier_cht.cpp"'
+# todo: add other navier miniapps
 '"nurbs"
   "NURBS miniapps:"
   "miniapps/nurbs"
   "nurbs_ex1.cpp nurbs_ex1p.cpp nurbs_ex11p.cpp"'
+# todo: add other nurbs miniapps
 '"shifted"
   "Shifted miniapps:"
   "miniapps/shifted"
   "distance.cpp"'
+# todo: add other shifted miniapps
 '"solvers"
   "Solvers miniapps:"
   "miniapps/solvers"
   "block-solvers.cpp"'
+# todo: add other solvers miniapps
+# todo: miniapps/spde
 '"tools"
   "Tools miniapps:"
   "miniapps/tools"
   "convert-dc.cpp display-basis.cpp get-values.cpp load-dc.cpp
    lor-transfer.cpp"'
+# todo: add other tools miniapps
 '"toys"
   "Toys miniapps:"
   "miniapps/toys"
@@ -386,7 +456,7 @@ function help_message()
      mfem_config [${mfem_config}]
         Set MFEM configuration options
      make [${make}], mpiexec [${mpiexec}], mpiexec_np [${mpiexec_np}]
-         Their values can also set using the respective uppercase environment
+         Their values can also be set using the respective uppercase environment
         variable
      mfem_build_dir [${mfem_build_dir}]
         Same as '-d': set this variable to something different from <mfem_dir>
@@ -18,9 +18,9 @@ elements
 boundary
 4
 1 1 0 1
-1 1 2 3
-1 1 3 0
-1 1 1 2
+2 1 2 3
+3 1 3 0
+4 1 1 2

 edges
 4
@@ -938,6 +938,7 @@ INPUT                  = @MFEM_SOURCE_DIR@/doc/CodeDocumentation.dox \
                         @MFEM_SOURCE_DIR@/config \
                         @MFEM_SOURCE_DIR@/general \
                         @MFEM_SOURCE_DIR@/linalg \
+                         @MFEM_SOURCE_DIR@/linalg/batched \
                         @MFEM_SOURCE_DIR@/linalg/simd \
                         @MFEM_SOURCE_DIR@/mesh \
                         @MFEM_SOURCE_DIR@/mesh/submesh \
@@ -1049,7 +1050,8 @@ RECURSIVE              = NO
 EXCLUDE                = @MFEM_SOURCE_DIR@/config/_config.hpp \
                         @MFEM_SOURCE_DIR@/config/get_hypre_version.cpp \
                         @MFEM_SOURCE_DIR@/general/tinyxml2.h \
-                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp
+                         @MFEM_SOURCE_DIR@/general/tinyxml2.cpp \
+                         @MFEM_SOURCE_DIR@/linalg/lapack.hpp

 # The EXCLUDE_SYMLINKS tag can be used to select whether or not files or
 # directories that are symbolic links (a Unix file system feature) are excluded
@@ -182,6 +182,21 @@ namespace mfem {
 *   <a class="el" href="examples_2superlu_2ex1p_8cpp_source.html">1p</a>,
 *   demonstrating the use of MFEM's \link superlu.hpp SuperLU integration\endlink.
 *
+ * <H4>NURBS Examples</H4>
+ * - Variants of Examples
+ *  <a class="el" href="nurbs__ex1_8cpp_source.html">1</a>,
+ *  <a class="el" href="nurbs__ex1p_8cpp_source.html">1p</a>,
+ *  <a class="el" href="nurbs__ex3_8cpp_source.html">3</a>,
+ *  <a class="el" href="nurbs__ex5_8cpp_source.html">5</a>,
+ *  <a class="el" href="nurbs__ex11p_8cpp_source.html">11p</a>, and
+ *  <a class="el" href="nurbs__ex24_8cpp_source.html">24</a>,
+ *   demonstrating howto perform NURBS-based Isogeometric Analysis.
+ * - Variant of Example <a class="el" href="nurbs__patch__ex1_8cpp_source.html">1</a>: demonstrates the use of patch integration
+ * - <a class="el" href="nurbs__solenoidal_8cpp_source.html">NURBS Divergence-free</a>: solve a solenoidal vector projection with NURBS-based H(div) elements
+ * - <a class="el" href="nurbs__curveint_8cpp_source.html">NURBS Interpolation</a>: NURBS interpolation of given geometry
+ * - <a class="el" href="nurbs__naca__cmesh_8cpp_source.html">NURBS NACA Mesher</a>: generate NURBS based mesh around a NACA foil
+ * - <a class="el" href="nurbs__printfunc_8cpp_source.html">NURBS Printer</a>: print the NURBS-basis
+ *
 * <H3>Miniapps</H3>
 * - <a class="el" href="volta_8cpp_source.html">Volta</a>: simple electrostatics simulation code
 * - <a class="el" href="tesla_8cpp_source.html">Tesla</a>: simple magnetostatics simulation code
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/amgx/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/caliper,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -87,16 +87,16 @@ public:
                        real_t visc, real_t mu, real_t K);

   /// Compute the right-hand side of the ODE system.
-   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
+   void Mult(const Vector &vx, Vector &dvx_dt) const override;
   /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;

   real_t ElasticEnergy(const Vector &x) const;
   real_t KineticEnergy(const Vector &v) const;
   void GetElasticEnergyDensity(const GridFunction &x, GridFunction &w) const;

-   virtual ~HyperelasticOperator();
+   ~HyperelasticOperator() override;
 };

 /** Nonlinear operator of the form:
@@ -120,12 +120,12 @@ public:
   void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);

   /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
-   virtual void Mult(const Vector &k, Vector &y) const;
+   void Mult(const Vector &k, Vector &y) const override;

   /// Compute J = M + dt S + dt^2 grad_H(x + dt (v + dt k)).
-   virtual Operator &GetGradient(const Vector &k) const;
+   Operator &GetGradient(const Vector &k) const override;

-   virtual ~ReducedSystemOperator();
+   ~ReducedSystemOperator() override;
 };


@@ -141,8 +141,8 @@ private:
 public:
   ElasticEnergyCoefficient(HyperelasticModel &m, const GridFunction &x_)
      : model(m), x(x_) { }
-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
-   virtual ~ElasticEnergyCoefficient() { }
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   ~ElasticEnergyCoefficient() override { }
 };

 void InitialDeformation(const Vector &x, Vector &y);
@@ -89,17 +89,17 @@ public:
                        real_t visc, real_t mu, real_t K);

   /// Compute the right-hand side of the ODE system.
-   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
+   void Mult(const Vector &vx, Vector &dvx_dt) const override;
   /** Solve the Backward-Euler equation: k = f(x + dt*k, t), for the unknown k.
       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;

   real_t ElasticEnergy(const ParGridFunction &x) const;
   real_t KineticEnergy(const ParGridFunction &v) const;
   void GetElasticEnergyDensity(const ParGridFunction &x,
                                ParGridFunction &w) const;

-   virtual ~HyperelasticOperator();
+   ~HyperelasticOperator() override;
 };

 /** Nonlinear operator of the form:
@@ -125,12 +125,12 @@ public:
   void SetParameters(real_t dt_, const Vector *v_, const Vector *x_);

   /// Compute y = H(x + dt (v + dt k)) + M k + S (v + dt k).
-   virtual void Mult(const Vector &k, Vector &y) const;
+   void Mult(const Vector &k, Vector &y) const override;

   /// Compute J = M + dt S + dt^2 grad_H(x + dt (v + dt k)).
-   virtual Operator &GetGradient(const Vector &k) const;
+   Operator &GetGradient(const Vector &k) const override;

-   virtual ~ReducedSystemOperator();
+   ~ReducedSystemOperator() override;
 };


@@ -146,8 +146,8 @@ private:
 public:
   ElasticEnergyCoefficient(HyperelasticModel &m, const ParGridFunction &x_)
      : model(m), x(x_) { }
-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
-   virtual ~ElasticEnergyCoefficient() { }
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
+   ~ElasticEnergyCoefficient() override { }
 };

 void InitialDeformation(const Vector &x, Vector &y);
@@ -53,7 +53,7 @@ public:
      pmesh(pmesh_),
      pgf(pgf_) {}

-   void MonitorSolution(int i, real_t norm, const Vector &x, bool final)
+   void MonitorSolution(int i, real_t norm, const Vector &x, bool final) override
   {
      char vishost[] = "localhost";
      int  visport   = 19916;
@@ -76,15 +76,15 @@ public:
   ConductionOperator(FiniteElementSpace &f, real_t alpha, real_t kappa,
                      const Vector &u);

-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   void Mult(const Vector &u, Vector &du_dt) const override;
   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
+   void ImplicitSolve(const real_t dt, const Vector &u, Vector &k) override;

   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
   void SetParameters(const Vector &u);

-   virtual ~ConductionOperator();
+   ~ConductionOperator() override;
 };

 real_t InitialTemperature(const Vector &x);
@@ -78,15 +78,15 @@ public:
   ConductionOperator(ParFiniteElementSpace &f, real_t alpha, real_t kappa,
                      const Vector &u);

-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   void Mult(const Vector &u, Vector &du_dt) const override;
   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const real_t dt, const Vector &u, Vector &k);
+   void ImplicitSolve(const real_t dt, const Vector &u, Vector &k) override;

   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
   void SetParameters(const Vector &u);

-   virtual ~ConductionOperator();
+   ~ConductionOperator() override;
 };

 real_t InitialTemperature(const Vector &x);
@@ -69,7 +69,7 @@ public:
   void SetDisplacement(GridFunction &u_) { u = &u_; }
   void SetComponent(int i, int j) { si = i; sj = j; }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 // Simple GLVis visualization manager.
@@ -89,7 +89,7 @@ public:
   void NewWindow();
   void CloseConnection();
   void PositionWindow();
-   virtual ~VisMan();
+   ~VisMan() override;
 };

 // Manipulators for the GLVis visualization manager.
@@ -69,7 +69,7 @@ public:
   void SetDisplacement(GridFunction &u_) { u = &u_; }
   void SetComponent(int i, int j) { si = i; sj = j; }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 // Simple GLVis visualization manager.
@@ -89,7 +89,7 @@ public:
   void NewWindow();
   void CloseConnection();
   void PositionWindow();
-   virtual ~VisMan();
+   ~VisMan() override;
 };

 // Manipulators for the GLVis visualization manager.
@@ -48,7 +48,7 @@ public:
      print_level = print_lvl;
   }

-   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
+   void MonitorResidual(int it, real_t norm, const Vector &r, bool final) override;

 private:
   const std::string prefix;
@@ -116,10 +116,10 @@ public:
   JacobianPreconditioner(Array<FiniteElementSpace *> &fes,
                          SparseMatrix &mass, Array<int> &offsets);

-   virtual void Mult(const Vector &k, Vector &y) const;
-   virtual void SetOperator(const Operator &op);
+   void Mult(const Vector &k, Vector &y) const override;
+   void SetOperator(const Operator &op) override;

-   virtual ~JacobianPreconditioner();
+   ~JacobianPreconditioner() override;
 };

 // After spatial discretization, the rubber model can be written as:
@@ -161,13 +161,13 @@ public:
                  int iter, Coefficient &mu);

   // Required to use the native newton solver
-   virtual Operator &GetGradient(const Vector &xp) const;
-   virtual void Mult(const Vector &k, Vector &y) const;
+   Operator &GetGradient(const Vector &xp) const override;
+   void Mult(const Vector &k, Vector &y) const override;

   // Driver for the newton solver
   void Solve(Vector &xp) const;

-   virtual ~RubberOperator();
+   ~RubberOperator() override;
 };

 // Visualization driver
@@ -62,7 +62,7 @@ public:
 #endif
   }

-   virtual void MonitorResidual(int it, real_t norm, const Vector &r, bool final);
+   void MonitorResidual(int it, real_t norm, const Vector &r, bool final) override;

 private:
   const std::string prefix;
@@ -130,10 +130,10 @@ public:
   JacobianPreconditioner(Array<ParFiniteElementSpace *> &fes,
                          Operator &mass, Array<int> &offsets);

-   virtual void Mult(const Vector &k, Vector &y) const;
-   virtual void SetOperator(const Operator &op);
+   void Mult(const Vector &k, Vector &y) const override;
+   void SetOperator(const Operator &op) override;

-   virtual ~JacobianPreconditioner();
+   ~JacobianPreconditioner() override;
 };

 // After spatial discretization, the rubber model can be written as:
@@ -175,13 +175,13 @@ public:
                  int iter, Coefficient &mu);

   // Required to use the native newton solver
-   virtual Operator &GetGradient(const Vector &xp) const;
-   virtual void Mult(const Vector &k, Vector &y) const;
+   Operator &GetGradient(const Vector &xp) const override;
+   void Mult(const Vector &k, Vector &y) const override;

   // Driver for the newton solver
   void Solve(Vector &xp) const;

-   virtual ~RubberOperator();
+   ~RubberOperator() override;
 };

 // Visualization driver
@@ -79,14 +79,14 @@ class GradT : public Operator
 {
 public:
   GradT() : Operator(1) {}
-   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
+   void Mult(const Vector &x, Vector &y) const override { y.Set(1.0/m_, x); }
 };

 class NegGradV : public TimeDependentOperator
 {
 public:
   NegGradV() : TimeDependentOperator(1) {}
-   void Mult(const Vector &x, Vector &y) const;
+   void Mult(const Vector &x, Vector &y) const override;
 };

 int main(int argc, char *argv[])
@@ -84,14 +84,14 @@ class GradT : public Operator
 {
 public:
   GradT() : Operator(1) {}
-   void Mult(const Vector &x, Vector &y) const { y.Set(1.0/m_, x); }
+   void Mult(const Vector &x, Vector &y) const override { y.Set(1.0/m_, x); }
 };

 class NegGradV : public TimeDependentOperator
 {
 public:
   NegGradV() : TimeDependentOperator(1) {}
-   void Mult(const Vector &x, Vector &y) const;
+   void Mult(const Vector &x, Vector &y) const override;
 };

 int main(int argc, char *argv[])
@@ -44,7 +44,7 @@ protected:
   BilinearForm *M;
   BilinearForm *K;

-   SparseMatrix Mmat, Kmat, Kmat0;
+   SparseMatrix Mmat, Kmat;
   SparseMatrix *T; // T = M + dt K
   real_t current_dt;

@@ -61,20 +61,20 @@ public:
   WaveOperator(FiniteElementSpace &f, Array<int> &ess_bdr, real_t speed);

   using SecondOrderTimeDependentOperator::Mult;
-   virtual void Mult(const Vector &u, const Vector &du_dt,
-                     Vector &d2udt2) const;
+   void Mult(const Vector &u, const Vector &du_dt,
+             Vector &d2udt2) const override;

   /** Solve the Backward-Euler equation:
       d2udt2 = f(u + fac0*d2udt2,dudt + fac1*d2udt2, t),
       for the unknown d2udt2. */
   using SecondOrderTimeDependentOperator::ImplicitSolve;
-   virtual void ImplicitSolve(const real_t fac0, const real_t fac1,
-                              const Vector &u, const Vector &dudt, Vector &d2udt2);
+   void ImplicitSolve(const real_t fac0, const real_t fac1,
+                      const Vector &u, const Vector &dudt, Vector &d2udt2) override;

   ///
   void SetParameters(const Vector &u);

-   virtual ~WaveOperator();
+   ~WaveOperator() override;
 };


@@ -83,25 +83,24 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
   : SecondOrderTimeDependentOperator(f.GetTrueVSize(), (real_t) 0.0),
     fespace(f), M(NULL), K(NULL), T(NULL), current_dt(0.0), z(height)
 {
-   const real_t rel_tol = 1e-8;
-
-   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
-
+   // Assemble Laplace matrix
   c2 = new ConstantCoefficient(speed*speed);
-
   K = new BilinearForm(&fespace);
   K->AddDomainIntegrator(new DiffusionIntegrator(*c2));
   K->Assemble();

-   Array<int> dummy;
-   K->FormSystemMatrix(dummy, Kmat0);
-   K->FormSystemMatrix(ess_tdof_list, Kmat);
-
+   // Assemble Mass matrix
   M = new BilinearForm(&fespace);
   M->AddDomainIntegrator(new MassIntegrator());
   M->Assemble();
+
+   // Apply Bcs
+   fespace.GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
+   K->FormSystemMatrix(ess_tdof_list, Kmat);
   M->FormSystemMatrix(ess_tdof_list, Mmat);

+   // Configure preconditioner
+   const real_t rel_tol = 1e-8;
   M_solver.iterative_mode = false;
   M_solver.SetRelTol(rel_tol);
   M_solver.SetAbsTol(0.0);
@@ -110,14 +109,13 @@ WaveOperator::WaveOperator(FiniteElementSpace &f,
   M_solver.SetPreconditioner(M_prec);
   M_solver.SetOperator(Mmat);

+   // Configure solver
   T_solver.iterative_mode = false;
   T_solver.SetRelTol(rel_tol);
   T_solver.SetAbsTol(0.0);
   T_solver.SetMaxIter(100);
   T_solver.SetPrintLevel(0);
   T_solver.SetPreconditioner(T_prec);
-
-   T = NULL;
 }

 void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
@@ -126,9 +124,11 @@ void WaveOperator::Mult(const Vector &u, const Vector &du_dt,
   // Compute:
   //    d2udt2 = M^{-1}*-K(u)
   // for d2udt2
-   Kmat.Mult(u, z);
+   K->FullMult(u, z);
   z.Neg(); // z = -z
+   z.SetSubVector(ess_tdof_list, 0.0);
   M_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }

 void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
@@ -142,14 +142,11 @@ void WaveOperator::ImplicitSolve(const real_t fac0, const real_t fac1,
      T = Add(1.0, Mmat, fac0, Kmat);
      T_solver.SetOperator(*T);
   }
-   Kmat0.Mult(u, z);
+   K->FullMult(u, z);
   z.Neg();
-
-   for (int i = 0; i < ess_tdof_list.Size(); i++)
-   {
-      z[ess_tdof_list[i]] = 0.0;
-   }
+   z.SetSubVector(ess_tdof_list, 0.0);
   T_solver.Mult(z, d2udt2);
+   d2udt2.SetSubVector(ess_tdof_list, 0.0);
 }

 void WaveOperator::SetParameters(const Vector &u)
@@ -314,7 +311,6 @@ int main(int argc, char *argv[])
         ess_bdr = 0;
      }
   }
-
   WaveOperator oper(fespace, ess_bdr, speed);

   u_gf.SetFromTrueDofs(u);
@@ -103,8 +103,8 @@ public:

   using VectorCoefficient::Eval;

-   virtual void Eval(Vector &K, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   {
      real_t x[3];
      Vector transip(x, 3);
@@ -102,8 +102,8 @@ public:

   using VectorCoefficient::Eval;

-   virtual void Eval(Vector &K, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   {
      real_t x[3];
      Vector transip(x, 3);
@@ -58,7 +58,7 @@ public:
      }
   }

-   virtual ~DiffusionMultigrid()
+   ~DiffusionMultigrid() override
   {
      delete amg;
   }
@@ -53,7 +53,7 @@ public:
                                    real_t min_val_=-36)
      : u(&u_), obstacle(&obst_), min_val(min_val_) { }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -69,7 +69,7 @@ public:
                                      real_t min_val_=0.0, real_t max_val_=1e6)
      : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 int main(int argc, char *argv[])
@@ -258,7 +258,7 @@ int main(int argc, char *argv[])
         MixedBilinearForm a10(&H1fes,&L2fes);
         a10.AddDomainIntegrator(new MixedScalarMassIntegrator());
         a10.Assemble();
-         a10.EliminateTrialDofs(ess_bdr, x.GetBlock(0), rhs.GetBlock(1));
+         a10.EliminateTrialEssentialBC(ess_bdr, x.GetBlock(0), rhs.GetBlock(1));
         a10.Finalize();
         SparseMatrix &A10 = a10.SpMat();

@@ -53,7 +53,7 @@ public:
                                    real_t min_val_=-36)
      : u(&u_), obstacle(&obst_), min_val(min_val_) { }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 class ExponentialGridFunctionCoefficient : public Coefficient
@@ -69,7 +69,7 @@ public:
                                      real_t min_val_=0.0, real_t max_val_=1e6)
      : u(&u_), obstacle(&obst_), min_val(min_val_), max_val(max_val_) { }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 int main(int argc, char *argv[])
@@ -52,8 +52,8 @@ public:
       fun(fun_) {}


-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   {
      return fun(GridFunctionCoefficient::Eval(T, ip));
   }
@@ -83,8 +83,8 @@ public:
       OtherGridF_cf(OtherGridF),
       fun(fun_) {}

-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   {
      const real_t value1 = fun(GridFunctionCoefficient::Eval(T, ip));
      const real_t value2 = fun(OtherGridF_cf.Eval(T, ip));
@@ -108,7 +108,7 @@ public:
      : rho_filter(rho_filter_), min_val(min_val_), max_val(max_val_),
        exponent(exponent_) { }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
   {
      real_t val = rho_filter->GetValue(T, ip);
      real_t coeff = min_val + pow(val,exponent)*(max_val-min_val);
@@ -142,7 +142,7 @@ public:
      MFEM_ASSERT(rho_filter, "density field is not set");
   }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
   {
      real_t L = lambda->Eval(T, ip);
      real_t M = mu->Eval(T, ip);
@@ -176,8 +176,8 @@ public:

   using VectorCoefficient::Eval;

-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   {
      Vector xx; xx.SetSize(T.GetDimension());
      T.Transform(ip,xx);
@@ -408,9 +408,9 @@ public:
    @param [in] Tr transformation of finite element
    @param [out] elvect vector containing the
   */
-   virtual void AssembleRHSElementVect(const FiniteElement &el,
-                                       ElementTransformation &Tr,
-                                       Vector &elvect) override
+   void AssembleRHSElementVect(const FiniteElement &el,
+                               ElementTransformation &Tr,
+                               Vector &elvect) override
   {
      int dof = el.GetDof();
      shape.SetSize(dof);
@@ -476,9 +476,9 @@ public:
    @param [in] Tr transformation of finite element
    @param [out] elvect vector containing the
   */
-   virtual void AssembleRHSElementVect(const FiniteElement &el,
-                                       ElementTransformation &Tr,
-                                       Vector &elvect) override
+   void AssembleRHSElementVect(const FiniteElement &el,
+                               ElementTransformation &Tr,
+                               Vector &elvect) override
   {
      int dof = el.GetDof();
      shape.SetSize(dof);
@@ -67,8 +67,10 @@ public:
   ZCoefficient(int vdim, GridFunction &psi_, real_t alpha_ = 1.0)
      : VectorCoefficient(vdim), psi(&psi_), alpha(alpha_) { }

-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };

@@ -82,8 +84,8 @@ public:
   DZCoefficient(int height, GridFunction &psi_, real_t alpha_ = 1.0)
      : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }

-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };

@@ -67,8 +67,10 @@ public:
   ZCoefficient(int vdim, ParGridFunction &psi_, real_t alpha_ = 1.0)
      : VectorCoefficient(vdim), psi(&psi_), alpha(alpha_) { }

-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   using VectorCoefficient::Eval;
+
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };

@@ -82,8 +84,8 @@ public:
   DZCoefficient(int height, ParGridFunction &psi_, real_t alpha_ = 1.0)
      : MatrixCoefficient(height),  psi(&psi_), alpha(alpha_) { }

-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   void SetAlpha(real_t alpha_) { alpha = alpha_; }
 };

@@ -157,7 +157,7 @@ int main(int argc, char *argv[])
   MixedBilinearForm *B0 = new MixedBilinearForm(x0_space,test_space);
   B0->AddDomainIntegrator(new DiffusionIntegrator(one));
   B0->Assemble();
-   B0->EliminateTrialDofs(ess_bdr, x.GetBlock(x0_var), F);
+   B0->EliminateTrialEssentialBC(ess_bdr, x.GetBlock(x0_var), F);
   B0->Finalize();

   MixedBilinearForm *Bhat = new MixedBilinearForm(xhat_space,test_space);
@@ -104,12 +104,12 @@ public:
      }
   }

-   void SetOperator(const Operator &op)
+   void SetOperator(const Operator &op) override
   {
      linear_solver.SetOperator(op);
   }

-   virtual void Mult(const Vector &x, Vector &y) const
+   void Mult(const Vector &x, Vector &y) const override
   {
      linear_solver.Mult(x, y);
   }
@@ -134,10 +134,10 @@ private:
 public:
   FE_Evolution(BilinearForm &M_, BilinearForm &K_, const Vector &b_);

-   virtual void Mult(const Vector &x, Vector &y) const;
-   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
+   void Mult(const Vector &x, Vector &y) const override;
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;

-   virtual ~FE_Evolution();
+   ~FE_Evolution() override;
 };


@@ -92,7 +92,7 @@ private:
 public:
   AIR_prec(int blocksize_) : AIR_solver(NULL), blocksize(blocksize_) { }

-   void SetOperator(const Operator &op)
+   void SetOperator(const Operator &op) override
   {
      width = op.Width();
      height = op.Height();
@@ -110,7 +110,7 @@ public:
      AIR_solver->SetMaxLevels(50);
   }

-   virtual void Mult(const Vector &x, Vector &y) const
+   void Mult(const Vector &x, Vector &y) const override
   {
      // Scale the rhs by block inverse and solve system
      HypreParVector z_s;
@@ -119,7 +119,7 @@ public:
      AIR_solver->Mult(z_s, y);
   }

-   ~AIR_prec()
+   ~AIR_prec() override
   {
      delete AIR_solver;
   }
@@ -185,17 +185,17 @@ public:
      }
   }

-   void SetOperator(const Operator &op)
+   void SetOperator(const Operator &op) override
   {
      linear_solver.SetOperator(op);
   }

-   virtual void Mult(const Vector &x, Vector &y) const
+   void Mult(const Vector &x, Vector &y) const override
   {
      linear_solver.Mult(x, y);
   }

-   ~DG_Solver()
+   ~DG_Solver() override
   {
      delete prec;
      delete A;
@@ -223,10 +223,10 @@ public:
   FE_Evolution(ParBilinearForm &M_, ParBilinearForm &K_, const Vector &b_,
                PrecType prec_type);

-   virtual void Mult(const Vector &x, Vector &y) const;
-   virtual void ImplicitSolve(const real_t dt, const Vector &x, Vector &k);
+   void Mult(const Vector &x, Vector &y) const override;
+   void ImplicitSolve(const real_t dt, const Vector &x, Vector &k) override;

-   virtual ~FE_Evolution();
+   ~FE_Evolution() override;
 };


@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/ginkgo/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -96,6 +96,7 @@ public:
   {
      Vector w_glob(width);
      pfes.Dof_TrueDof_Matrix()->MultTranspose(w, w_glob);
+      w_glob.HostReadWrite(); // read+write -> can use w_glob(i) (non-const)
      for (int i = 0; i < width; i++) { grad(0, i) = w_glob(i); }
   }

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/hiop/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ..
 MFEM_BUILD_DIR ?= ..
+MFEM_INSTALL_DIR ?= ../mfem
 SRC = $(if $(MFEM_DIR:..=),$(MFEM_DIR)/examples/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/moonolith/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -206,6 +206,7 @@ int main(int argc, char *argv[])
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool petsc_use_jfnk = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -243,6 +244,8 @@ int main(int argc, char *argv[])
   args.AddOption(&petsc_use_jfnk, "-jfnk", "--jfnk", "-no-jfnk",
                  "--no-jfnk",
                  "Use JFNK with user-defined preconditioner factory.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -257,7 +260,12 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 2b. We initialize PETSc
+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
   if (use_petsc)
   {
      MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL);
@@ -67,6 +67,7 @@ int main(int argc, char *argv[])
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool use_nonoverlapping = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -95,6 +96,8 @@ int main(int argc, char *argv[])
                  "-no-nonoverlapping", "--no-nonoverlapping",
                  "Use or not the block diagonal PETSc's matrix format "
                  "for non-overlapping domain decomposition.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -109,7 +112,12 @@ int main(int argc, char *argv[])
      args.PrintOptions(cout);
   }

-   // 2b. We initialize PETSc
+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }

   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -61,6 +61,7 @@ int main(int argc, char *argv[])
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool use_nonoverlapping = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -87,6 +88,8 @@ int main(int argc, char *argv[])
                  "-no-nonoverlapping", "--no-nonoverlapping",
                  "Use or not the block diagonal PETSc's matrix format "
                  "for non-overlapping domain decomposition.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -100,10 +103,16 @@ int main(int argc, char *argv[])
   {
      args.PrintOptions(cout);
   }
-   // 2b. We initialize PETSc
-   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
   kappa = freq * M_PI;

+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
+
   // 3. 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.
@@ -58,6 +58,7 @@ int main(int argc, char *argv[])
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool use_nonoverlapping = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -88,6 +89,8 @@ int main(int argc, char *argv[])
                  "-no-nonoverlapping", "--no-nonoverlapping",
                  "Use or not the block diagonal PETSc's matrix format "
                  "for non-overlapping domain decomposition.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -101,10 +104,16 @@ int main(int argc, char *argv[])
   {
      args.PrintOptions(cout);
   }
-   // 2b. We initialize PETSc
-   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
   kappa = freq * M_PI;

+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
+   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }
+
   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
   //    can handle triangular, quadrilateral, tetrahedral, hexahedral, surface
   //    and volume, as well as periodic meshes with the same code.
@@ -59,6 +59,8 @@ int main(int argc, char *argv[])

   // 2. Parse command-line options.
   const char *mesh_file = "../../data/star.mesh";
+   int ser_ref_levels = -1;
+   int par_ref_levels = 2;
   int order = 1;
   bool par_format = false;
   bool visualization = 1;
@@ -66,15 +68,22 @@ int main(int argc, char *argv[])
   bool use_nonoverlapping = false;
   bool local_bdr_spec = false;
   const char *petscrc_file = "";
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
                  "Mesh file to use.");
+   args.AddOption(&ser_ref_levels, "-rs", "--refine-serial",
+                  "Number of times to refine the mesh uniformly in serial.");
+   args.AddOption(&par_ref_levels, "-rp", "--refine-parallel",
+                  "Number of times to refine the mesh uniformly in parallel.");
   args.AddOption(&order, "-o", "--order",
                  "Finite element order (polynomial degree).");
   args.AddOption(&par_format, "-pf", "--parallel-format", "-sf",
                  "--serial-format",
                  "Format to use when saving the results for VisIt.");
+   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.");
@@ -103,7 +112,13 @@ int main(int argc, char *argv[])
   {
      args.PrintOptions(cout);
   }
-   // 2b. We initialize PETSc
+
+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }

   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -117,9 +132,11 @@ int main(int argc, char *argv[])
   //    'ref_levels' to be the largest number that gives a final mesh with no
   //    more than 10,000 elements.
   {
-      int ref_levels =
-         (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
-      for (int l = 0; l < ref_levels; l++)
+      if (ser_ref_levels < 0)
+      {
+         ser_ref_levels = (int)floor(log(10000./mesh->GetNE())/log(2.)/dim);
+      }
+      for (int l = 0; l < ser_ref_levels; l++)
      {
         mesh->UniformRefinement();
      }
@@ -131,7 +148,6 @@ int main(int argc, char *argv[])
   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();
@@ -187,21 +203,26 @@ int main(int argc, char *argv[])

   // 9. Define the parallel grid function and parallel linear forms, solution
   //    vector and rhs.
-   BlockVector x(block_offsets), rhs(block_offsets);
-   BlockVector trueX(block_trueOffsets), trueRhs(block_trueOffsets);
+   MemoryType mt = device.GetMemoryType();
+   BlockVector x(block_offsets, mt), rhs(block_offsets, mt);
+   BlockVector trueX(block_trueOffsets, mt), trueRhs(block_trueOffsets, mt);

   ParLinearForm *fform(new ParLinearForm);
   fform->Update(R_space, rhs.GetBlock(0), 0);
   fform->AddDomainIntegrator(new VectorFEDomainLFIntegrator(fcoeff));
   fform->AddBoundaryIntegrator(new VectorFEBoundaryFluxLFIntegrator(fnatcoeff));
   fform->Assemble();
+   fform->SyncAliasMemory(rhs);
   fform->ParallelAssemble(trueRhs.GetBlock(0));
+   trueRhs.GetBlock(0).SyncAliasMemory(trueRhs);

   ParLinearForm *gform(new ParLinearForm);
   gform->Update(W_space, rhs.GetBlock(1), 0);
   gform->AddDomainIntegrator(new DomainLFIntegrator(gcoeff));
   gform->Assemble();
+   gform->SyncAliasMemory(rhs);
   gform->ParallelAssemble(trueRhs.GetBlock(1));
+   trueRhs.GetBlock(1).SyncAliasMemory(trueRhs);

   // 10. Assemble the finite element matrices for the Darcy operator
   //
@@ -53,6 +53,7 @@ int main(int argc, char *argv[])
   bool use_petsc = true;
   const char *petscrc_file = "";
   bool use_nonoverlapping = false;
+   const char *device_config = "cpu";

   OptionsParser args(argc, argv);
   args.AddOption(&mesh_file, "-m", "--mesh",
@@ -73,6 +74,8 @@ int main(int argc, char *argv[])
                  "-no-nonoverlapping", "--no-nonoverlapping",
                  "Use or not the block diagonal PETSc's matrix format "
                  "for non-overlapping domain decomposition.");
+   args.AddOption(&device_config, "-d", "--device",
+                  "Device configuration string, see Device::Configure().");
   args.Parse();
   if (!args.Good())
   {
@@ -86,7 +89,13 @@ int main(int argc, char *argv[])
   {
      args.PrintOptions(cout);
   }
-   // 2b. We initialize PETSc
+
+   // 2b. 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(); }
+
+   // 2c. We initialize PETSc
   if (use_petsc) { MFEMInitializePetsc(NULL,NULL,petscrc_file,NULL); }

   // 3. Read the (serial) mesh from the given mesh file on all processors.  We
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/petsc/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -66,7 +66,6 @@ int main(int argc, char *argv[])
 {
   // 1. Initialize MPI (required by PUMI) and HYPRE.
   Mpi::Init(argc, argv);
-   int num_procs = Mpi::WorldSize();
   int myid = Mpi::WorldRank();
   Hypre::Init();

@@ -80,8 +80,6 @@ int main(int argc, char *argv[])
 {
   // 1. Initialize MPI (required by PUMI) and HYPRE.
   Mpi::Init(argc, argv);
-   int num_proc = Mpi::WorldSize();
-   int myId = Mpi::WorldRank();
   Hypre::Init();

   // 2. Parse command-line options.
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/pumi/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -31,11 +31,21 @@ include_directories(BEFORE ${PROJECT_BINARY_DIR})
 add_custom_target(test_sundials
  ${CMAKE_CTEST_COMMAND} -R sundials USES_TERMINAL)

-# Add one executable per cpp file, adding "sundials_" as prefix. Sets
-# "test_sundials" as a target that depends on the given examples.
+# Add one executable per cpp file, adding "sundials_" as prefix so the CMake
+# target is unique from those in the non-SUNDIALS examples. Also sets
+# "test_sundials" as a target that depends on the given SUNDIALS examples.
 set(PFX sundials_)
 add_mfem_examples(SUNDIALS_EXAMPLES_SRCS ${PFX} "" test_sundials)

+# Remove "sundials_" prefix from exectuable name for consistency with GNU build
+# system.
+foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})
+  get_filename_component(SRC_FILENAME ${SRC_FILE} NAME)
+  string(REPLACE ".cpp" "" TARGET_NAME "${PFX}${SRC_FILENAME}")
+  string(REPLACE ${PFX} "" EXE_NAME ${TARGET_NAME})
+  set_target_properties(${TARGET_NAME} PROPERTIES OUTPUT_NAME ${EXE_NAME})
+endforeach()
+
 # Testing.
 # The SUNDIALS tests can be run separately using the target "test_sundials"
 # which builds the examples and runs:
@@ -51,7 +61,10 @@ if (MFEM_ENABLE_TESTING)
  set(EX10_COMMON_OPTS -m ../../data/beam-quad.mesh -o 2 -s 5 -dt 0.15 -tf 6 -vs 10)
  set(EX10_TEST_OPTS ${EX10_COMMON_OPTS}  -r  2)
  set(EX10P_TEST_OPTS ${EX10_COMMON_OPTS} -rp 1)
-  # Example 16: use the default options
+  # Example 16: test ARKODE with implicit time stepping using mass form
+  set(EX16_COMMON_OPTS -s 15)
+  set(EX16_TEST_OPTS ${EX16_COMMON_OPTS})
+  set(EX16P_TEST_OPTS ${EX16_COMMON_OPTS})

  # Add the tests: one test per source file.
  foreach(SRC_FILE ${SUNDIALS_EXAMPLES_SRCS})
@@ -1,15 +1,17 @@
 //                                MFEM Example 10
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10
+// Compile with:
+//    make ex10             (GNU make)
+//    make sundials_ex10    (CMake)
 //
 // Sample runs:
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 12 -dt 0.15 -vs 10
 //    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 16 -dt 0.3  -vs 5
 //    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 12 -dt 0.2  -vs 5
-//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  2 -dt 3 -nls kinsol
-//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  2 -dt 3 -nls kinsol
-//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  2 -dt 3 -nls kinsol
+//    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s  2 -dt 3 -nls 1
+//    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s  2 -dt 3 -nls 2
+//    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s  2 -dt 3 -nls 4
 //    ex10 -m ../../data/beam-quad.mesh -r 2 -o 2 -s 14 -dt 0.15 -vs 10
 //    ex10 -m ../../data/beam-tri.mesh  -r 2 -o 2 -s 17 -dt 0.01 -vs 30
 //    ex10 -m ../../data/beam-hex.mesh  -r 1 -o 2 -s 14 -dt 0.15 -vs 10
@@ -97,16 +99,11 @@ protected:
   double saved_gamma; // saved gamma value from implicit setup

 public:
-   /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
-   enum NonlinearSolverType
-   {
-      NEWTON = 0, ///< Use MFEM's plain NewtonSolver
-      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
-   };

   HyperelasticOperator(FiniteElementSpace &f, Array<int> &ess_bdr,
                        double visc, double mu, double K,
-                        NonlinearSolverType nls_type);
+                        int kinsol_nls_type = -1, double kinsol_damping = 0.0,
+                        int kinsol_aa_n = 0);

   /// Compute the right-hand side of the ODE system.
   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -224,8 +221,10 @@ int main(int argc, char *argv[])
   double mu = 0.25;
   double K = 5.0;
   bool visualization = true;
-   const char *nls = "newton";
+   int nonlinear_solver_type = 0;
   int vis_steps = 1;
+   double kinsol_damping = 0.0;
+   int kinsol_aa_n = -1;

   // Relative and absolute tolerances for CVODE and ARKODE.
   const double reltol = 1e-1, abstol = 1e-1;
@@ -262,9 +261,18 @@ int main(int argc, char *argv[])
                  "15 - ARKODE implicit, approximate Jacobian,\n\t"
                  "16 - ARKODE implicit, specified Jacobian,\n\t"
                  "17 - ARKODE explicit, 4th order.");
-   args.AddOption(&nls, "-nls", "--nonlinear-solver",
-                  "Nonlinear systems solver: "
-                  "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
+   args.AddOption(&nonlinear_solver_type, "-nls", "--nonlinear-solver",
+                  "Nonlinear system solver:\n\t"
+                  "0  - MFEM Newton method,\n\t"
+                  "1  - KINSOL Newton method,\n\t"
+                  "2  - KINSOL Newton method with globalization,\n\t"
+                  "3  - KINSOL fixed-point method (with or without AA),\n\t"
+                  "4  - KINSOL Picard method (with or without AA).");
+   args.AddOption(&kinsol_damping, "-damp", "--kinsol-damping",
+                  "Picard or Fixed-Point damping parameter (only valid with KINSOL): "
+                  "0 < d <= 1.0");
+   args.AddOption(&kinsol_aa_n, "-aan", "--anderson-subspace",
+                  "Anderson Acceleration subspace size (only valid with KINSOL)");
   args.AddOption(&t_final, "-tf", "--t-final",
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
@@ -295,22 +303,32 @@ int main(int argc, char *argv[])
      return 1;
   }

+   // check for valid nonlinear solver options
+   if (nonlinear_solver_type < 0 || nonlinear_solver_type > 4)
+   {
+      cout << "Unknown nonlinear solver type: " << nonlinear_solver_type << "\n";
+      return 1;
+   }
+   if (kinsol_damping > 0.0 &&
+       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
+   {
+      cout << "Only KINSOL fixed-point and Picard methods can use damping\n";
+      return 1;
+   }
+   if (kinsol_aa_n > 0 &&
+       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
+   {
+      cout << "Only KINSOL fixed-point and Picard methods can use AA\n";
+      return 1;
+   }
+
+
   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 3. Setup the nonlinear solver
-   map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
-   nls_map["newton"] = HyperelasticOperator::NEWTON;
-   nls_map["kinsol"] = HyperelasticOperator::KINSOL;
-   if (nls_map.find(nls) == nls_map.end())
-   {
-      cout << "Unknown type of nonlinear solver: " << nls << endl;
-      return 4;
-   }
-
-   // 4. Refine the mesh to increase the resolution. In this example we do
+   // 3. Refine the mesh to increase the resolution. In this example we do
   //    'ref_levels' of uniform refinement, where 'ref_levels' is a
   //    command-line parameter.
   for (int lev = 0; lev < ref_levels; lev++)
@@ -318,7 +336,7 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 5. Define the vector finite element spaces representing the mesh
+   // 4. Define the vector finite element spaces representing the mesh
   //    deformation x, the velocity v, and the initial configuration, x_ref.
   //    Define also the elastic energy density, w, which is in a discontinuous
   //    higher-order space. Since x and v are integrated in time as a system,
@@ -346,7 +364,7 @@ int main(int argc, char *argv[])
   FiniteElementSpace w_fespace(mesh, &w_fec);
   GridFunction w(&w_fespace);

-   // 6. Set the initial conditions for v and x, and the boundary conditions on
+   // 5. Set the initial conditions for v and x, and the boundary conditions on
   //    a beam-like mesh (see description above).
   VectorFunctionCoefficient velo(dim, InitialVelocity);
   v.ProjectCoefficient(velo);
@@ -359,9 +377,34 @@ int main(int argc, char *argv[])
   ess_bdr = 0;
   ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed

-   // 7. Initialize the hyperelastic operator, the GLVis visualization and print
+   // 6. Initialize the hyperelastic operator, the GLVis visualization and print
   //    the initial energies.
-   HyperelasticOperator oper(fespace, ess_bdr, visc, mu, K, nls_map[nls]);
+   std::unique_ptr<HyperelasticOperator> oper;
+   if (nonlinear_solver_type == 0)
+      oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr, visc, mu,
+                                                    K);
+   else
+   {
+      switch (nonlinear_solver_type)
+      {
+         case 1:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_NONE);
+            break;
+         case 2:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_LINESEARCH);
+            break;
+         case 3:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_FP, kinsol_damping, kinsol_aa_n);
+            break;
+         case 4:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_PICARD, kinsol_damping, kinsol_aa_n);
+            break;
+      }
+   }

   socketstream vis_v, vis_w;
   if (visualization)
@@ -375,23 +418,23 @@ int main(int argc, char *argv[])
      vis_w.open(vishost, visport);
      if (vis_w)
      {
-         oper.GetElasticEnergyDensity(x, w);
+         oper->GetElasticEnergyDensity(x, w);
         vis_w.precision(8);
         visualize(vis_w, mesh, &x, &w, "Elastic energy density", true);
      }
   }

-   double ee0 = oper.ElasticEnergy(x.GetTrueVector());
-   double ke0 = oper.KineticEnergy(v.GetTrueVector());
+   double ee0 = oper->ElasticEnergy(x.GetTrueVector());
+   double ke0 = oper->KineticEnergy(v.GetTrueVector());
   cout << "initial elastic energy (EE) = " << ee0 << endl;
   cout << "initial kinetic energy (KE) = " << ke0 << endl;
   cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;

-   // 8. Define the ODE solver used for time integration. Several implicit
+   // 7. Define the ODE solver used for time integration. Several implicit
   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
   //    explicit Runge-Kutta methods are available.
   double t = 0.0;
-   oper.SetTime(t);
+   oper->SetTime(t);

   ODESolver *ode_solver = NULL;
   CVODESolver *cvode = NULL;
@@ -415,7 +458,7 @@ int main(int argc, char *argv[])
      case 11:
      case 12:
         cvode = new CVODESolver(CV_BDF);
-         cvode->Init(oper);
+         cvode->Init(*oper);
         cvode->SetSStolerances(reltol, abstol);
         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
         cvode->SetMaxStep(dt);
@@ -428,7 +471,7 @@ int main(int argc, char *argv[])
      case 13:
      case 14:
         cvode = new CVODESolver(CV_ADAMS);
-         cvode->Init(oper);
+         cvode->Init(*oper);
         cvode->SetSStolerances(reltol, abstol);
         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
         cvode->SetMaxStep(dt);
@@ -441,7 +484,7 @@ int main(int argc, char *argv[])
      case 15:
      case 16:
         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
+         arkode->Init(*oper);
         arkode->SetSStolerances(reltol, abstol);
         ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
         arkode->SetMaxStep(dt);
@@ -453,16 +496,16 @@ int main(int argc, char *argv[])
      // ARKStep Explicit methods
      case 17:
         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
-         arkode->Init(oper);
+         arkode->Init(*oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
         ode_solver = arkode; break;
   }

   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
-   if (ode_solver_type < 11) { ode_solver->Init(oper); }
+   if (ode_solver_type < 11) { ode_solver->Init(*oper); }

-   // 9. Perform time-integration (looping over the time iterations, ti, with a
+   // 8. Perform time-integration (looping over the time iterations, ti, with a
   //    time-step dt).
   bool last_step = false;
   for (int ti = 1; !last_step; ti++)
@@ -475,8 +518,8 @@ int main(int argc, char *argv[])

      if (last_step || (ti % vis_steps) == 0)
      {
-         double ee = oper.ElasticEnergy(x.GetTrueVector());
-         double ke = oper.KineticEnergy(v.GetTrueVector());
+         double ee = oper->ElasticEnergy(x.GetTrueVector());
+         double ke = oper->KineticEnergy(v.GetTrueVector());

         cout << "step " << ti << ", t = " << t << ", EE = " << ee << ", KE = "
              << ke << ", ΔTE = " << (ee+ke)-(ee0+ke0) << endl;
@@ -490,14 +533,14 @@ int main(int argc, char *argv[])
            visualize(vis_v, mesh, &x, &v);
            if (vis_w)
            {
-               oper.GetElasticEnergyDensity(x, w);
+               oper->GetElasticEnergyDensity(x, w);
               visualize(vis_w, mesh, &x, &w);
            }
         }
      }
   }

-   // 10. Save the displaced mesh, the velocity and elastic energy.
+   // 9. Save the displaced mesh, the velocity and elastic energy.
   {
      v.SetFromTrueVector(); x.SetFromTrueVector();
      GridFunction *nodes = &x;
@@ -512,11 +555,11 @@ int main(int argc, char *argv[])
      v.Save(velo_ofs);
      ofstream ee_ofs("elastic_energy.sol");
      ee_ofs.precision(8);
-      oper.GetElasticEnergyDensity(x, w);
+      oper->GetElasticEnergyDensity(x, w);
      w.Save(ee_ofs);
   }

-   // 11. Free the used memory.
+   // 10. Free the used memory.
   delete ode_solver;
   delete mesh;

@@ -600,7 +643,9 @@ ReducedSystemOperator::~ReducedSystemOperator()
 HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
                                           Array<int> &ess_bdr, double visc,
                                           double mu, double K,
-                                           NonlinearSolverType nls_type)
+                                           int kinsol_nls_type,
+                                           double kinsol_damping,
+                                           int kinsol_aa_n)
   : TimeDependentOperator(2*f.GetTrueVSize(), 0.0), fespace(f),
     M(&fespace), S(&fespace), H(&fespace),
     viscosity(visc), z(height/2),
@@ -651,15 +696,28 @@ HyperelasticOperator::HyperelasticOperator(FiniteElementSpace &f,
   J_prec = NULL;
 #endif

-   if (nls_type == KINSOL)
+   if (kinsol_nls_type > 0)
   {
-      KINSolver *kinsolver = new KINSolver(KIN_NONE, true);
+      KINSolver *kinsolver = new KINSolver(kinsol_nls_type, true);
+      if (kinsol_nls_type != KIN_PICARD)
+      {
+         kinsolver->SetJFNK(true);
+         kinsolver->SetLSMaxIter(100);
+      }
+      if (kinsol_aa_n > 0)
+      {
+         kinsolver->EnableAndersonAcc(kinsol_aa_n);
+      }
      newton_solver = kinsolver;
      newton_solver->SetOperator(*reduced_oper);
      newton_solver->SetMaxIter(200);
      newton_solver->SetRelTol(rel_tol);
      newton_solver->SetPrintLevel(0);
      kinsolver->SetMaxSetupCalls(4);
+      if (kinsol_damping > 0.0)
+      {
+         kinsolver->SetDamping(kinsol_damping);
+      }
   }
   else
   {
@@ -1,15 +1,17 @@
 //                       MFEM Example 10 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex10p
+// Compile with:
+//    make ex10p            (GNU make)
+//    make sundials_ex10p   (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 12 -dt 0.15 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 16 -dt 0.25 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 12 -dt 0.15 -vs 10
-//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
-//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  2 -dt 3 -nls kinsol
-//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rs 1 -o 2 -s  2 -dt 3 -nls kinsol
+//    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s  2 -dt 3 -nls 1
+//    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s  2 -dt 3 -nls 2
+//    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rs 1 -o 2 -s  2 -dt 3 -nls 4
 //    mpirun -np 4 ex10p -m ../../data/beam-quad.mesh -rp 1 -o 2 -s 14 -dt 0.15 -vs 10
 //    mpirun -np 4 ex10p -m ../../data/beam-tri.mesh  -rp 1 -o 2 -s 17 -dt 5e-3 -vs 60
 //    mpirun -np 4 ex10p -m ../../data/beam-hex.mesh  -rp 0 -o 2 -s 14 -dt 0.15 -vs 10
@@ -99,16 +101,11 @@ protected:
   double saved_gamma; // saved gamma value from implicit setup

 public:
-   /// Solver type to use in the ImplicitSolve() method, used by SDIRK methods.
-   enum NonlinearSolverType
-   {
-      NEWTON = 0, ///< Use MFEM's plain NewtonSolver
-      KINSOL = 1  ///< Use SUNDIALS' KINSOL (through MFEM's class KINSolver)
-   };

   HyperelasticOperator(ParFiniteElementSpace &f, Array<int> &ess_bdr,
                        double visc, double mu, double K,
-                        NonlinearSolverType nls_type);
+                        int kinsol_nls_type = -1, double kinsol_damping = 0.0,
+                        int kinsol_aa_n = 0);

   /// Compute the right-hand side of the ODE system.
   virtual void Mult(const Vector &vx, Vector &dvx_dt) const;
@@ -233,8 +230,10 @@ int main(int argc, char *argv[])
   double mu = 0.25;
   double K = 5.0;
   bool visualization = true;
-   const char *nls = "newton";
+   int nonlinear_solver_type = 0;
   int vis_steps = 1;
+   double kinsol_damping = 0.0;
+   int kinsol_aa_n = -1;

   // Relative and absolute tolerances for CVODE and ARKODE.
   const double reltol = 1e-1, abstol = 1e-1;
@@ -273,9 +272,18 @@ int main(int argc, char *argv[])
                  "15 - ARKODE implicit, approximate Jacobian,\n\t"
                  "16 - ARKODE implicit, specified Jacobian,\n\t"
                  "17 - ARKODE explicit, 4th order.");
-   args.AddOption(&nls, "-nls", "--nonlinear-solver",
-                  "Nonlinear systems solver: "
-                  "\"newton\" (plain Newton) or \"kinsol\" (KINSOL).");
+   args.AddOption(&nonlinear_solver_type, "-nls", "--nonlinear-solver",
+                  "Nonlinear system solver:\n\t"
+                  "0  - MFEM Newton method,\n\t"
+                  "1  - KINSOL Newton method,\n\t"
+                  "2  - KINSOL Newton method with globalization,\n\t"
+                  "3  - KINSOL fixed-point method (with or without AA),\n\t"
+                  "4  - KINSOL Picard method (with or without AA).");
+   args.AddOption(&kinsol_damping, "-damp", "--kinsol-damping",
+                  "Picard or Fixed-Point damping parameter (only valid with KINSOL): "
+                  "0 < d <= 1.0");
+   args.AddOption(&kinsol_aa_n, "-aan", "--anderson-subspace",
+                  "Anderson Acceleration subspace size (only valid with KINSOL)");
   args.AddOption(&t_final, "-tf", "--t-final",
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
@@ -315,27 +323,42 @@ int main(int argc, char *argv[])
      return 1;
   }

+   // check for valid nonlinear solver options
+   if (nonlinear_solver_type < 0 || nonlinear_solver_type > 4)
+   {
+      if (myid == 0)
+      {
+         cout << "Unknown nonlinear solver type: " << nonlinear_solver_type
+              << "\n";
+      }
+      return 1;
+   }
+   if (kinsol_damping > 0.0 &&
+       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
+   {
+      if (myid == 0)
+      {
+         cout << "Only KINSOL fixed-point and Picard methods can use damping\n";
+      }
+      return 1;
+   }
+   if (kinsol_aa_n > 0 &&
+       !(nonlinear_solver_type == 3 || nonlinear_solver_type == 4))
+   {
+      if (myid == 0)
+      {
+         cout << "Only KINSOL fixed-point and Picard methods can use AA\n";
+      }
+      return 1;
+   }
+
   // 3. Read the serial mesh from the given mesh file on all processors. We can
   //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
   //    with the same code.
   Mesh *mesh = new Mesh(mesh_file, 1, 1);
   int dim = mesh->Dimension();

-   // 4. Nonlinear solver
-   map<string,HyperelasticOperator::NonlinearSolverType> nls_map;
-   nls_map["newton"] = HyperelasticOperator::NEWTON;
-   nls_map["kinsol"] = HyperelasticOperator::KINSOL;
-   if (nls_map.find(nls) == nls_map.end())
-   {
-      if (myid == 0)
-      {
-         cout << "Unknown type of nonlinear solver: " << nls << endl;
-      }
-      delete mesh;
-      return 4;
-   }
-
-   // 5. Refine the mesh in serial to increase the resolution. In this example
+   // 4. Refine the mesh in serial to increase the resolution. In this example
   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
   //    a command-line parameter.
   for (int lev = 0; lev < ser_ref_levels; lev++)
@@ -343,7 +366,7 @@ int main(int argc, char *argv[])
      mesh->UniformRefinement();
   }

-   // 6. Define a parallel mesh by a partitioning of the serial mesh. Refine
+   // 5. 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);
@@ -353,7 +376,7 @@ int main(int argc, char *argv[])
      pmesh->UniformRefinement();
   }

-   // 7. Define the parallel vector finite element spaces representing the mesh
+   // 6. Define the parallel vector finite element spaces representing the mesh
   //    deformation x_gf, the velocity v_gf, and the initial configuration,
   //    x_ref. Define also the elastic energy density, w_gf, which is in a
   //    discontinuous higher-order space. Since x and v are integrated in time
@@ -385,7 +408,7 @@ int main(int argc, char *argv[])
   ParFiniteElementSpace w_fespace(pmesh, &w_fec);
   ParGridFunction w_gf(&w_fespace);

-   // 8. Set the initial conditions for v_gf, x_gf and vx, and define the
+   // 7. Set the initial conditions for v_gf, x_gf and vx, and define the
   //    boundary conditions on a beam-like mesh (see description above).
   VectorFunctionCoefficient velo(dim, InitialVelocity);
   v_gf.ProjectCoefficient(velo);
@@ -400,9 +423,38 @@ int main(int argc, char *argv[])
   ess_bdr = 0;
   ess_bdr[0] = 1; // boundary attribute 1 (index 0) is fixed

-   // 9. Initialize the hyperelastic operator, the GLVis visualization and print
+   // 8. Initialize the hyperelastic operator, the GLVis visualization and print
   //    the initial energies.
-   HyperelasticOperator oper(fespace, ess_bdr, visc, mu, K, nls_map[nls]);
+   std::unique_ptr<HyperelasticOperator> oper;
+   if (nonlinear_solver_type == 0)
+      oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr, visc, mu,
+                                                    K);
+   else
+   {
+      switch (nonlinear_solver_type)
+      {
+         case 1:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_NONE);
+            break;
+         case 2:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_LINESEARCH);
+            break;
+         case 3:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_FP, kinsol_damping, kinsol_aa_n);
+            break;
+         case 4:
+            oper = std::make_unique<HyperelasticOperator>(fespace, ess_bdr,
+                                                          visc, mu, K, KIN_PICARD, kinsol_damping, kinsol_aa_n);
+            break;
+         default:
+            cout << "Unknown type of nonlinear solver: "
+                 << nonlinear_solver_type << endl;
+            return 4;
+      }
+   }

   socketstream vis_v, vis_w;
   if (visualization)
@@ -418,14 +470,14 @@ int main(int argc, char *argv[])
      vis_w.open(vishost, visport);
      if (vis_w)
      {
-         oper.GetElasticEnergyDensity(x_gf, w_gf);
+         oper->GetElasticEnergyDensity(x_gf, w_gf);
         vis_w.precision(8);
         visualize(vis_w, pmesh, &x_gf, &w_gf, "Elastic energy density", true);
      }
   }

-   double ee0 = oper.ElasticEnergy(x_gf);
-   double ke0 = oper.KineticEnergy(v_gf);
+   double ee0 = oper->ElasticEnergy(x_gf);
+   double ke0 = oper->KineticEnergy(v_gf);
   if (myid == 0)
   {
      cout << "initial elastic energy (EE) = " << ee0 << endl;
@@ -433,11 +485,11 @@ int main(int argc, char *argv[])
      cout << "initial   total energy (TE) = " << (ee0 + ke0) << endl;
   }

-   // 10. Define the ODE solver used for time integration. Several implicit
-   //     singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
-   //     explicit Runge-Kutta methods are available.
+   // 9. Define the ODE solver used for time integration. Several implicit
+   //    singly diagonal implicit Runge-Kutta (SDIRK) methods, as well as
+   //    explicit Runge-Kutta methods are available.
   double t = 0.0;
-   oper.SetTime(t);
+   oper->SetTime(t);

   ODESolver *ode_solver = NULL;
   CVODESolver *cvode = NULL;
@@ -461,7 +513,7 @@ int main(int argc, char *argv[])
      case 11:
      case 12:
         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
-         cvode->Init(oper);
+         cvode->Init(*oper);
         cvode->SetSStolerances(reltol, abstol);
         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
         cvode->SetMaxStep(dt);
@@ -474,7 +526,7 @@ int main(int argc, char *argv[])
      case 13:
      case 14:
         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
-         cvode->Init(oper);
+         cvode->Init(*oper);
         cvode->SetSStolerances(reltol, abstol);
         CVodeSetEpsLin(cvode->GetMem(), cvode_eps_lin);
         cvode->SetMaxStep(dt);
@@ -487,7 +539,7 @@ int main(int argc, char *argv[])
      case 15:
      case 16:
         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
+         arkode->Init(*oper);
         arkode->SetSStolerances(reltol, abstol);
         ARKStepSetNonlinConvCoef(arkode->GetMem(), arkode_eps_nonlin);
         arkode->SetMaxStep(dt);
@@ -499,16 +551,16 @@ int main(int argc, char *argv[])
      // ARKStep Explicit methods
      case 17:
         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
-         arkode->Init(oper);
+         arkode->Init(*oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
         ode_solver = arkode; break;
   }

   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
-   if (ode_solver_type < 11) { ode_solver->Init(oper); }
+   if (ode_solver_type < 11) { ode_solver->Init(*oper); }

-   // 11. Perform time-integration
+   // 10. Perform time-integration
   //     (looping over the time iterations, ti, with a time-step dt).
   bool last_step = false;
   for (int ti = 1; !last_step; ti++)
@@ -523,8 +575,8 @@ int main(int argc, char *argv[])
      {
         v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();

-         double ee = oper.ElasticEnergy(x_gf);
-         double ke = oper.KineticEnergy(v_gf);
+         double ee = oper->ElasticEnergy(x_gf);
+         double ke = oper->KineticEnergy(v_gf);

         if (myid == 0)
         {
@@ -540,14 +592,14 @@ int main(int argc, char *argv[])
            visualize(vis_v, pmesh, &x_gf, &v_gf);
            if (vis_w)
            {
-               oper.GetElasticEnergyDensity(x_gf, w_gf);
+               oper->GetElasticEnergyDensity(x_gf, w_gf);
               visualize(vis_w, pmesh, &x_gf, &w_gf);
            }
         }
      }
   }

-   // 12. Save the displaced mesh, the velocity and elastic energy.
+   // 11. Save the displaced mesh, the velocity and elastic energy.
   {
      v_gf.SetFromTrueVector(); x_gf.SetFromTrueVector();
      GridFunction *nodes = &x_gf;
@@ -568,11 +620,11 @@ int main(int argc, char *argv[])
      v_gf.Save(velo_ofs);
      ofstream ee_ofs(ee_name.str().c_str());
      ee_ofs.precision(8);
-      oper.GetElasticEnergyDensity(x_gf, w_gf);
+      oper->GetElasticEnergyDensity(x_gf, w_gf);
      w_gf.Save(ee_ofs);
   }

-   // 13. Free the used memory.
+   // 12. Free the used memory.
   delete ode_solver;
   delete pmesh;

@@ -662,7 +714,10 @@ ReducedSystemOperator::~ReducedSystemOperator()
 HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
                                           Array<int> &ess_bdr, double visc,
                                           double mu, double K,
-                                           NonlinearSolverType nls_type)
+                                           int kinsol_nls_type,
+                                           double kinsol_damping,
+                                           int kinsol_aa_n)
+
   : TimeDependentOperator(2*f.TrueVSize(), 0.0), fespace(f),
     M(&fespace), S(&fespace), H(&fespace),
     viscosity(visc), M_solver(f.GetComm()), z(height/2),
@@ -714,17 +769,28 @@ HyperelasticOperator::HyperelasticOperator(ParFiniteElementSpace &f,
   J_minres->SetPreconditioner(*J_prec);
   J_solver = J_minres;

-   if (nls_type == KINSOL)
+   if (kinsol_nls_type > 0)
   {
-      KINSolver *kinsolver = new KINSolver(f.GetComm(), KIN_LINESEARCH, true);
-      kinsolver->SetJFNK(true);
-      kinsolver->SetLSMaxIter(100);
+      KINSolver *kinsolver = new KINSolver(f.GetComm(), kinsol_nls_type, true);
+      if (kinsol_nls_type != KIN_PICARD)
+      {
+         kinsolver->SetJFNK(true);
+         kinsolver->SetLSMaxIter(100);
+      }
+      if (kinsol_aa_n > 0)
+      {
+         kinsolver->EnableAndersonAcc(kinsol_aa_n);
+      }
      newton_solver = kinsolver;
      newton_solver->SetOperator(*reduced_oper);
      newton_solver->SetMaxIter(200);
      newton_solver->SetRelTol(rel_tol);
-      newton_solver->SetPrintLevel(1);
+      newton_solver->SetPrintLevel(0);
      kinsolver->SetMaxSetupCalls(4);
+      if (kinsol_damping > 0.0)
+      {
+         kinsolver->SetDamping(kinsol_damping);
+      }
   }
   else
   {
@@ -1,15 +1,21 @@
 //                                MFEM Example 16
 //                             SUNDIALS Modification
 //
-// Compile with: make ex16
+// Compile with:
+//    make ex16             (GNU make)
+//    make sundials_ex16    (CMake)
 //
 // Sample runs:  ex16
 //               ex16 -m ../../data/inline-tri.mesh
 //               ex16 -m ../../data/disc-nurbs.mesh -tf 2
 //               ex16 -s 12 -a 0.0 -k 1.0
+//               ex16 -s 15 -a 0.0 -k 1.0
 //               ex16 -s 8 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
+//               ex16 -s 11 -a 1.0 -k 0.0 -dt 1e-4 -tf 5e-2 -vs 25
 //               ex16 -s 9 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
+//               ex16 -s 12 -a 0.5 -k 0.5 -o 4 -dt 1e-4 -tf 2e-2 -vs 25
 //               ex16 -s 10 -dt 1.0e-4 -tf 4.0e-2 -vs 40
+//               ex16 -s 13 -dt 1.0e-4 -tf 4.0e-2 -vs 40
 //               ex16 -m ../../data/fichera-q2.mesh
 //               ex16 -m ../../data/escher.mesh
 //               ex16 -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -37,75 +43,102 @@
 using namespace std;
 using namespace mfem;

-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
 *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
 *
 *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
 *  (\kappa + \alpha u).
 *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
 */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
   FiniteElementSpace &fespace;
   Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.

-   BilinearForm *M;
-   BilinearForm *K;
+   BilinearForm M;
+   SparseMatrix Mmat;

-   SparseMatrix Mmat, Kmat;
-   SparseMatrix *T; // T = M + dt K
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
+   SparseMatrix Kmat;
+
+   std::unique_ptr<SparseMatrix> T; // T = M + gam K(u)

   CGSolver M_solver; // Krylov solver for inverting the mass matrix M
   DSmoother M_prec;  // Preconditioner for the mass matrix M

-   CGSolver T_solver; // Implicit solver for T = M + dt K
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
   DSmoother T_prec;  // Preconditioner for the implicit solver

-   double alpha, kappa;
-
   mutable Vector z; // auxiliary vector

 public:
-   ConductionOperator(FiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);

-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(FiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);

-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);

-   /// Custom Jacobian system solver for the SUNDIALS time integrators.
-   /** For the ODE system represented by ConductionOperator
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+    operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+      approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;

-           M du/dt = -K(u),
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;

-       this class facilitates the solution of linear systems of the form
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;

-           (M + γK) y = M b,
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;

-       for given b, u (not used), and γ = GetTimeStep(). */
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;

-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   int SUNMassSetup() override;

-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;

-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
-
-   virtual ~ConductionOperator();
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };

-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+

 int main(int argc, char *argv[])
 {
@@ -117,16 +150,16 @@ int main(int argc, char *argv[])
   int ref_levels = 2;
   int order = 2;
   int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
   bool visualization = true;
   bool visit = false;
   int vis_steps = 5;

   // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;

   int precision = 8;
   cout.precision(precision);
@@ -151,7 +184,10 @@ int main(int argc, char *argv[])
                  "9  - CVODE (implicit BDF),\n\t"
                  "10 - ARKODE (default explicit),\n\t"
                  "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
   args.AddOption(&t_final, "-tf", "--t-final",
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
@@ -174,16 +210,13 @@ int main(int argc, char *argv[])
      args.PrintUsage(cout);
      return 1;
   }
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      return 3;
-   }
   args.PrintOptions(cout);

+   bool use_mass_solver = ode_solver_type >= 13;
+
   // 2. Read the mesh from the given mesh file. We can handle triangular,
   //    quadrilateral, tetrahedral and hexahedral meshes with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
+   std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 1));
   int dim = mesh->Dimension();

   // 3. Refine the mesh to increase the resolution. In this example we do
@@ -197,7 +230,7 @@ int main(int argc, char *argv[])
   // 4. Define the vector finite element space representing the current and the
   //    initial temperature, u_ref.
   H1_FECollection fe_coll(order, dim);
-   FiniteElementSpace fespace(mesh, &fe_coll);
+   FiniteElementSpace fespace(mesh.get(), &fe_coll);

   int fe_size = fespace.GetTrueVSize();
   cout << "Number of temperature unknowns: " << fe_size << endl;
@@ -211,8 +244,17 @@ int main(int argc, char *argv[])
   Vector u;
   u_gf.GetTrueDofs(u);

-   // 6. Initialize the conduction operator and the visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 6. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);

   u_gf.SetFromTrueDofs(u);
   {
@@ -224,7 +266,7 @@ int main(int argc, char *argv[])
      u_gf.Save(osol);
   }

-   VisItDataCollection visit_dc("Example16", mesh);
+   VisItDataCollection visit_dc("Example16", mesh.get());
   visit_dc.RegisterField("temperature", &u_gf);
   if (visit)
   {
@@ -258,52 +300,75 @@ int main(int argc, char *argv[])
   }

   // 7. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
   switch (ode_solver_type)
   {
      // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
      // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
      // CVODE
      case 8:
-         cvode = new CVODESolver(CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
      case 9:
-         cvode = new CVODESolver(CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(new CVODESolver(cvode_solver_type));
         cvode->Init(oper);
         cvode->SetSStolerances(reltol, abstol);
         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
      // ARKODE
      case 10:
      case 11:
-         arkode = new ARKStepSolver(ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(arkode_solver_type));
         arkode->Init(oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
         {
            arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
         }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
   }

   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -311,8 +376,14 @@ int main(int argc, char *argv[])

   // Since we want to update the diffusion coefficient after every time step,
   // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }

   // 8. Perform time-integration (looping over the time iterations, ti, with a
   //    time-step dt).
@@ -323,7 +394,7 @@ int main(int argc, char *argv[])
   bool last_step = false;
   for (int ti = 1; !last_step; ti++)
   {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);

      // Note that since we are using the "one-step" mode of the SUNDIALS
      // solvers, they will, generally, step over the final time and will not
@@ -337,8 +408,14 @@ int main(int argc, char *argv[])
      if (last_step || (ti % vis_steps) == 0)
      {
         cout << "step " << ti << ", t = " << t << endl;
-         if (cvode) { cvode->PrintInfo(); }
-         if (arkode) { arkode->PrintInfo(); }
+         if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+         {
+            cvode->PrintInfo();
+         }
+         else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+         {
+            arkode->PrintInfo();
+         }

         u_gf.SetFromTrueDofs(u);
         if (visualization)
@@ -353,137 +430,153 @@ int main(int argc, char *argv[])
            visit_dc.Save();
         }
      }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
   }
   tic_toc.Stop();
   cout << "Done, " << tic_toc.RealTime() << "s." << endl;

   // 9. Save the final solution. This output can be viewed later using GLVis:
   //    "glvis -m ex16.mesh -g ex16-final.gf".
-   {
-      ofstream osol("ex16-final.gf");
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 10. Free the used memory.
-   delete ode_solver;
-   delete mesh;
+   u_gf.Save("ex16-final.gf", precision);

   return 0;
 }

-ConductionOperator::ConductionOperator(FiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL), z(height)
+ConductionOperator::ConductionOperator(FiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;

-   M = new BilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble();
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble();
+   M.FormSystemMatrix(ess_tdof_list, Mmat);

   M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
   M_solver.SetAbsTol(0.0);
   M_solver.SetMaxIter(50);
   M_solver.SetPrintLevel(0);
   M_solver.SetPreconditioner(M_prec);
   M_solver.SetOperator(Mmat);

-   alpha = al;
-   kappa = kap;
-
   T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
   T_solver.SetAbsTol(0.0);
   T_solver.SetMaxIter(100);
   T_solver.SetPrintLevel(0);
   T_solver.SetPreconditioner(T_prec);

-   SetParameters(u);
+   SetConductionTensor(u);
 }

-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
   GridFunction u_alpha_gf(&fespace);
   u_alpha_gf.SetFromTrueDofs(u);
   for (int i = 0; i < u_alpha_gf.Size(); i++)
   {
      u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
   }
-
-   delete K;
-   K = new BilinearForm(&fespace);
-
   GridFunctionCoefficient u_coeff(&u_alpha_gf);

+   K = std::make_unique<BilinearForm>(&fespace);
   K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
   K->Assemble();
   K->FormSystemMatrix(ess_tdof_list, Kmat);
 }

-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
+}
+
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
+{
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
   T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
+   T_solver.Mult(z, k);
 }

-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
 {
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<SparseMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
 }

-ConductionOperator::~ConductionOperator()
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
 {
-   delete T;
-   delete M;
-   delete K;
-}
-
-double InitialTemperature(const Vector &x)
-{
-   if (x.Norml2() < 0.5)
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
   {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
   }
   else
   {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
   }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}
+
@@ -1,16 +1,22 @@
 //                         MFEM Example 16 - Parallel Version
 //                              SUNDIALS Modification
 //
-// Compile with: make ex16p
+// Compile with:
+//    make ex16p            (GNU make)
+//    make sundials_ex16p   (CMake)
 //
 // Sample runs:
 //     mpirun -np 4 ex16p
 //     mpirun -np 4 ex16p -m ../../data/inline-tri.mesh
 //     mpirun -np 4 ex16p -m ../../data/disc-nurbs.mesh -tf 2
 //     mpirun -np 4 ex16p -s 12 -a 0.0 -k 1.0
+//     mpirun -np 4 ex16p -s 15 -a 0.0 -k 1.0
 //     mpirun -np 4 ex16p -s 8 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
+//     mpirun -np 4 ex16p -s 11 -a 1.0 -k 0.0 -dt 4e-6 -tf 2e-2 -vs 50
 //     mpirun -np 8 ex16p -s 9 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
+//     mpirun -np 8 ex16p -s 12 -a 0.5 -k 0.5 -o 4 -dt 8e-6 -tf 2e-2 -vs 50
 //     mpirun -np 4 ex16p -s 10 -dt 2.0e-4 -tf 4.0e-2
+//     mpirun -np 4 ex16p -s 13 -dt 2.0e-4 -tf 4.0e-2
 //     mpirun -np 16 ex16p -m ../../data/fichera-q2.mesh
 //     mpirun -np 16 ex16p -m ../../data/escher-p2.mesh
 //     mpirun -np 8 ex16p -m ../../data/beam-tet.mesh -tf 10 -dt 0.1
@@ -38,66 +44,102 @@
 using namespace std;
 using namespace mfem;

-/** After spatial discretization, the conduction model can be written as:
+/** After spatial discretization, the conduction model is expressed as
 *
- *     du/dt = M^{-1}(-Ku)
+ *   M du/dt = - K(u) u
 *
 *  where u is the vector representing the temperature, M is the mass matrix,
- *  and K is the diffusion operator with diffusivity depending on u:
+ *  and K(u) is the diffusion operator with diffusivity depending on u:
 *  (\kappa + \alpha u).
 *
- *  Class ConductionOperator represents the right-hand side of the above ODE.
+ *  Class ConductionOperatorOperator represents the above ODE operator in the
+ *  general form F(u, k, t) = G(u, t) where either
+ *
+ *    1. F(u, du/dt, t) = du/dt            (ODE is expressed in EXPLICIT form)
+ *       G(u, t) = - inv(M) K(u) u
+ *    2. F(u, du/dt, t) = M du/dt          (ODE is expressed in IMPLICIT form)
+ *       G(u, t) = - K(u) u
 */
 class ConductionOperator : public TimeDependentOperator
 {
-protected:
   ParFiniteElementSpace &fespace;
   Array<int> ess_tdof_list; // this list remains empty for pure Neumann b.c.

-   ParBilinearForm *M;
-   ParBilinearForm *K;
-
+   ParBilinearForm M;
   HypreParMatrix Mmat;
+
+   const real_t alpha, kappa;
+   std::unique_ptr<BilinearForm> K;
   HypreParMatrix Kmat;
-   HypreParMatrix *T; // T = M + dt K
-   double current_dt;

-   CGSolver M_solver;    // Krylov solver for inverting the mass matrix M
-   HypreSmoother M_prec; // Preconditioner for the mass matrix M
+   std::unique_ptr<HypreParMatrix> T; // T = M + gam K(u)

-   CGSolver T_solver;    // Implicit solver for T = M + dt K
-   HypreSmoother T_prec; // Preconditioner for the implicit solver
+   CGSolver M_solver; // Krylov solver for inverting the mass matrix M
+   HypreSmoother M_prec;  // Preconditioner for the mass matrix M

-   double alpha, kappa;
+   CGSolver T_solver; // Implicit solver for T = M + gam K(u)
+   HypreSmoother T_prec;  // Preconditioner for the implicit solver

   mutable Vector z; // auxiliary vector

 public:
-   ConductionOperator(ParFiniteElementSpace &f, double alpha, double kappa,
-                      const Vector &u);

-   virtual void Mult(const Vector &u, Vector &du_dt) const;
+   ConductionOperator(ParFiniteElementSpace &f, const real_t alpha,
+                      const real_t kappa, const Vector &u,
+                      const Type &ode_expression_type);

-   /** Solve the Backward-Euler equation: k = f(u + dt*k, t), for the unknown k.
-       This is the only requirement for high-order SDIRK implicit integration.*/
-   virtual void ImplicitSolve(const double dt, const Vector &u, Vector &k);
+   // Compute K(u_n) for use as an approximation in - K(u) u
+   void SetConductionTensor(const Vector &u);

-   /** Setup the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSetup(const Vector &x, const Vector &fx,
-                                int jok, int *jcur, double gamma);
+   /** Compute G(u, t) as defined in the IMPLICIT expression form of the ODE
+       operator, i.e., @a v = - K(u_n) @a u. Note that K(u_n) is an
+       approximation to K(u). */
+   void ExplicitMult(const Vector &u, Vector &v) const override;

-   /** Solve the system (M + dt K) x = M b. This method is used by the implicit
-       SUNDIALS solvers. */
-   virtual int SUNImplicitSolve(const Vector &b, Vector &x, double tol);
+   /** Solve for k in F(u, k, t) = G(u, t) for either EXPLICIT or IMPLICIT
+       expression forms of the ODE operator, i.e., @a k = - inv(M) K(u_n) @a u.
+       Note that K(u_n) is an approximation to K(u). */
+   void Mult(const Vector &u, Vector &k) const override;

-   /// Update the diffusion BilinearForm K using the given true-dof vector `u`.
-   void SetParameters(const Vector &u);
+   /** Solve for k in F(u + gam*k, k, t) = G(u + gam*k, t) for either EXPLICIT
+       or IMPLICIT expression forms of the ODE operator, i.e.,
+       [ M + @a gam K(u_n) ] @a k = - K(u_n) @a u . Note that K(u_n) is an
+       approximation to K(u). */
+   void ImplicitSolve(const real_t gam, const Vector &u, Vector &k) override;

-   virtual ~ConductionOperator();
+   /** Setup to solve for dk in [dF/dk + gam*dF/du - gam*dG/du] dk = G - F for
+       either EXPLICIT or IMPLICIT expression forms of the ODE operator, i.e.,
+       [M - @a gam Jf(u)] dk = G - F, where Jf(u) is an approximation of the
+       Jacobian of -K(u) u. The approximation chosen here is Jf(u) = -K(u_n). */
+   int SUNImplicitSetup(const Vector &u, const Vector &fu, int jok, int *jcur,
+                        real_t gam) override;
+
+   /** Solve for @a dk in the system in SUNImplicitSetup to the given tolerance,
+       with the residual @a r providing either
+        1. @a r = G - F = inv(M) f(u) - k       (EXPLICIT expression form)
+        1. @a r = G - F = f(u) - M k            (IMPLICIT expression form)
+       */
+   int SUNImplicitSolve(const Vector &r, Vector &dk, real_t tol) override;
+
+   int SUNMassSetup() override;
+
+   int SUNMassSolve(const Vector &b, Vector &x, real_t tol) override;
+
+   int SUNMassMult(const Vector &x, Vector &v) override;
 };

-double InitialTemperature(const Vector &x);
+real_t InitialTemperature(const Vector &x)
+{
+   if (x.Norml2() < 0.5)
+   {
+      return 2.0;
+   }
+   else
+   {
+      return 1.0;
+   }
+}
+

 int main(int argc, char *argv[])
 {
@@ -114,16 +156,16 @@ int main(int argc, char *argv[])
   int par_ref_levels = 1;
   int order = 2;
   int ode_solver_type = 9; // CVODE implicit BDF
-   double t_final = 0.5;
-   double dt = 1.0e-2;
-   double alpha = 1.0e-2;
-   double kappa = 0.5;
+   real_t t_final = 0.5;
+   real_t dt = 1.0e-2;
+   real_t alpha = 1.0e-2;
+   real_t kappa = 0.5;
   bool visualization = true;
   bool visit = false;
   int vis_steps = 5;

   // Relative and absolute tolerances for CVODE and ARKODE.
-   const double reltol = 1e-4, abstol = 1e-4;
+   const real_t reltol = 1e-4, abstol = 1e-4;

   int precision = 8;
   cout.precision(precision);
@@ -150,7 +192,10 @@ int main(int argc, char *argv[])
                  "9  - CVODE (implicit BDF),\n\t"
                  "10 - ARKODE (default explicit),\n\t"
                  "11 - ARKODE (explicit Fehlberg-6-4-5),\n\t"
-                  "12 - ARKODE (default impicit).");
+                  "12 - ARKODE (default implicit),\n\t"
+                  "13 - ARKODE (default explicit with MFEM mass solve),\n\t"
+                  "14 - ARKODE (explicit Fehlberg-6-4-5 with MFEM mass solve),\n\t"
+                  "15 - ARKODE (default implicit with MFEM mass solve).");
   args.AddOption(&t_final, "-tf", "--t-final",
                  "Final time; start time is 0.");
   args.AddOption(&dt, "-dt", "--time-step",
@@ -174,40 +219,33 @@ int main(int argc, char *argv[])
      return 1;
   }

-   if (myid == 0)
+   if (Mpi::Root())
   {
      args.PrintOptions(cout);
   }

-   // check for valid ODE solver option
-   if (ode_solver_type < 1 || ode_solver_type > 12)
-   {
-      if (myid == 0)
-      {
-         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
-      }
-      return 1;
-   }
+   bool use_mass_solver = ode_solver_type >= 13;

-   // 3. Read the serial mesh from the given mesh file on all processors. We can
+   // 3. Define a parallel mesh by a partitioning of a serial mesh. Read the
+   //    serial mesh from the given mesh file on all processors. We can
   //    handle triangular, quadrilateral, tetrahedral and hexahedral meshes
   //    with the same code.
-   Mesh *mesh = new Mesh(mesh_file, 1, 1);
-   int dim = mesh->Dimension();
-
-   // 4. Refine the mesh in serial to increase the resolution. In this example
-   //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
-   //    a command-line parameter.
-   for (int lev = 0; lev < ser_ref_levels; lev++)
+   std::unique_ptr<ParMesh> pmesh;
   {
-      mesh->UniformRefinement();
-   }
+      std::unique_ptr<Mesh> mesh(new Mesh(mesh_file, 1, 1));

-   // 5. 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;
+      // 4. Refine the mesh in serial to increase the resolution. In this example
+      //    we do 'ser_ref_levels' of uniform refinement, where 'ser_ref_levels' is
+      //    a command-line parameter.
+      for (int lev = 0; lev < ser_ref_levels; lev++)
+      {
+         mesh->UniformRefinement();
+      }
+
+      // 5. Refine this mesh further in parallel to increase the resolution.
+      //    Once the parallel mesh is defined, the serial mesh can be deleted.
+      pmesh = std::make_unique<ParMesh>(MPI_COMM_WORLD, *mesh);
+   }
   for (int lev = 0; lev < par_ref_levels; lev++)
   {
      pmesh->UniformRefinement();
@@ -215,8 +253,9 @@ int main(int argc, char *argv[])

   // 6. Define the vector finite element space representing the current and the
   //    initial temperature, u_ref.
+   int dim = pmesh->Dimension();
   H1_FECollection fe_coll(order, dim);
-   ParFiniteElementSpace fespace(pmesh, &fe_coll);
+   ParFiniteElementSpace fespace(pmesh.get(), &fe_coll);

   int fe_size = fespace.GlobalTrueVSize();
   if (myid == 0)
@@ -233,8 +272,17 @@ int main(int argc, char *argv[])
   Vector u;
   u_gf.GetTrueDofs(u);

-   // 8. Initialize the conduction operator and the VisIt visualization.
-   ConductionOperator oper(fespace, alpha, kappa, u);
+   // 8. Initialize the conduction ODE operator and the visualization.
+   ConductionOperator::Type ode_expression_type;
+   if (use_mass_solver)
+   {
+      ode_expression_type = ConductionOperator::Type::IMPLICIT;
+   }
+   else
+   {
+      ode_expression_type = ConductionOperator::Type::EXPLICIT;
+   }
+   ConductionOperator oper(fespace, alpha, kappa, u, ode_expression_type);

   u_gf.SetFromTrueDofs(u);
   {
@@ -249,7 +297,7 @@ int main(int argc, char *argv[])
      u_gf.Save(osol);
   }

-   VisItDataCollection visit_dc("Example16-Parallel", pmesh);
+   VisItDataCollection visit_dc("Example16-Parallel", pmesh.get());
   visit_dc.RegisterField("temperature", &u_gf);
   if (visit)
   {
@@ -293,52 +341,76 @@ int main(int argc, char *argv[])
   }

   // 9. Define the ODE solver used for time integration.
-   double t = 0.0;
-   ODESolver *ode_solver = NULL;
-   CVODESolver *cvode = NULL;
-   ARKStepSolver *arkode = NULL;
+   real_t t = 0.0;
+   std::unique_ptr<ODESolver> ode_solver;
   switch (ode_solver_type)
   {
      // MFEM explicit methods
-      case 1: ode_solver = new ForwardEulerSolver; break;
-      case 2: ode_solver = new RK2Solver(0.5); break; // midpoint method
-      case 3: ode_solver = new RK3SSPSolver; break;
-      case 4: ode_solver = new RK4Solver; break;
+      case 1: ode_solver = std::make_unique<ForwardEulerSolver>(); break;
+      case 2: ode_solver = std::make_unique<RK2Solver>(0.5); break; // midpoint method
+      case 3: ode_solver = std::make_unique<RK3SSPSolver>(); break;
+      case 4: ode_solver = std::make_unique<RK4Solver>(); break;
      // MFEM implicit L-stable methods
-      case 5: ode_solver = new BackwardEulerSolver; break;
-      case 6: ode_solver = new SDIRK23Solver(2); break;
-      case 7: ode_solver = new SDIRK33Solver; break;
+      case 5: ode_solver = std::make_unique<BackwardEulerSolver>(); break;
+      case 6: ode_solver = std::make_unique<SDIRK23Solver>(2); break;
+      case 7: ode_solver = std::make_unique<SDIRK33Solver>(); break;
      // CVODE
      case 8:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_ADAMS);
-         cvode->Init(oper);
-         cvode->SetSStolerances(reltol, abstol);
-         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
      case 9:
-         cvode = new CVODESolver(MPI_COMM_WORLD, CV_BDF);
+      {
+         int cvode_solver_type;
+         if (ode_solver_type == 8)
+         {
+            cvode_solver_type = CV_ADAMS;
+         }
+         else
+         {
+            cvode_solver_type = CV_BDF;
+         }
+         std::unique_ptr<CVODESolver> cvode(
+            new CVODESolver(MPI_COMM_WORLD, cvode_solver_type));
         cvode->Init(oper);
         cvode->SetSStolerances(reltol, abstol);
         cvode->SetMaxStep(dt);
-         ode_solver = cvode; break;
+         ode_solver = std::move(cvode);
+         break;
+      }
      // ARKODE
      case 10:
      case 11:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::EXPLICIT);
+      case 12:
+      case 13:
+      case 14:
+      case 15:
+      {
+         ARKStepSolver::Type arkode_solver_type;
+         if (ode_solver_type == 12 || ode_solver_type == 15)
+         {
+            arkode_solver_type = ARKStepSolver::IMPLICIT;
+         }
+         else
+         {
+            arkode_solver_type = ARKStepSolver::EXPLICIT;
+         }
+         std::unique_ptr<ARKStepSolver> arkode(
+            new ARKStepSolver(MPI_COMM_WORLD, arkode_solver_type));
         arkode->Init(oper);
         arkode->SetSStolerances(reltol, abstol);
         arkode->SetMaxStep(dt);
-         if (ode_solver_type == 11)
+         if (ode_solver_type == 11 || ode_solver_type == 14)
         {
            arkode->SetERKTableNum(ARKODE_FEHLBERG_13_7_8);
         }
-         ode_solver = arkode; break;
-      case 12:
-         arkode = new ARKStepSolver(MPI_COMM_WORLD, ARKStepSolver::IMPLICIT);
-         arkode->Init(oper);
-         arkode->SetSStolerances(reltol, abstol);
-         arkode->SetMaxStep(dt);
-         ode_solver = arkode; break;
+         if (use_mass_solver)
+         {
+            arkode->UseMFEMMassLinearSolver(SUNFALSE);
+         }
+         ode_solver = std::move(arkode);
+         break;
+      }
+      default:
+         cout << "Unknown ODE solver type: " << ode_solver_type << '\n';
+         return 3;
   }

   // Initialize MFEM integrators, SUNDIALS integrators are initialized above
@@ -346,12 +418,18 @@ int main(int argc, char *argv[])

   // Since we want to update the diffusion coefficient after every time step,
   // we need to use the "one-step" mode of the SUNDIALS solvers.
-   if (cvode) { cvode->SetStepMode(CV_ONE_STEP); }
-   if (arkode) { arkode->SetStepMode(ARK_ONE_STEP); }
+   if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+   {
+      cvode->SetStepMode(CV_ONE_STEP);
+   }
+   else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+   {
+      arkode->SetStepMode(ARK_ONE_STEP);
+   }

   // 10. Perform time-integration (looping over the time iterations, ti, with a
   //     time-step dt).
-   if (myid == 0)
+   if (Mpi::Root())
   {
      cout << "Integrating the ODE ..." << endl;
   }
@@ -361,7 +439,7 @@ int main(int argc, char *argv[])
   bool last_step = false;
   for (int ti = 1; !last_step; ti++)
   {
-      double dt_real = min(dt, t_final - t);
+      real_t dt_real = min(dt, t_final - t);

      // Note that since we are using the "one-step" mode of the SUNDIALS
      // solvers, they will, generally, step over the final time and will not
@@ -377,8 +455,14 @@ int main(int argc, char *argv[])
         if (myid == 0)
         {
            cout << "step " << ti << ", t = " << t << endl;
-            if (cvode) { cvode->PrintInfo(); }
-            if (arkode) { arkode->PrintInfo(); }
+            if (CVODESolver* cvode = dynamic_cast<CVODESolver*>(ode_solver.get()))
+            {
+               cvode->PrintInfo();
+            }
+            else if (ARKStepSolver* arkode = dynamic_cast<ARKStepSolver*>(ode_solver.get()))
+            {
+               arkode->PrintInfo();
+            }
         }

         u_gf.SetFromTrueDofs(u);
@@ -395,46 +479,38 @@ int main(int argc, char *argv[])
            visit_dc.Save();
         }
      }
-      oper.SetParameters(u);
+      oper.SetConductionTensor(u);
   }
   tic_toc.Stop();
-   if (myid == 0)
+   if (Mpi::Root())
   {
      cout << "Done, " << tic_toc.RealTime() << "s." << endl;
   }

   // 11. Save the final solution in parallel. This output can be viewed later
   //     using GLVis: "glvis -np <np> -m ex16-mesh -g ex16-final".
-   {
-      ostringstream sol_name;
-      sol_name << "ex16-final." << setfill('0') << setw(6) << myid;
-      ofstream osol(sol_name.str().c_str());
-      osol.precision(precision);
-      u_gf.Save(osol);
-   }
-
-   // 12. Free the used memory.
-   delete ode_solver;
-   delete pmesh;
+   u_gf.Save("ex16-final", precision);

   return 0;
 }

-ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
-                                       double kap, const Vector &u)
-   : TimeDependentOperator(f.GetTrueVSize(), 0.0), fespace(f), M(NULL), K(NULL),
-     T(NULL),
-     M_solver(f.GetComm()), T_solver(f.GetComm()), z(height)
+ConductionOperator::ConductionOperator(ParFiniteElementSpace &fes,
+                                       const real_t alpha, const real_t kappa,
+                                       const Vector &u,
+                                       const Type &ode_expression_type)
+   : TimeDependentOperator(fes.GetTrueVSize(), 0.0, ode_expression_type),
+     fespace(fes), alpha(alpha), kappa(kappa), M(&fespace),
+     M_solver(fes.GetComm()), T_solver(fes.GetComm()), z(height)
 {
-   const double rel_tol = 1e-8;
+   // specify a relative tolerance for all solves with MFEM integrators
+   const real_t rel_tol = 1e-8;

-   M = new ParBilinearForm(&fespace);
-   M->AddDomainIntegrator(new MassIntegrator());
-   M->Assemble(0); // keep sparsity pattern of M and K the same
-   M->FormSystemMatrix(ess_tdof_list, Mmat);
+   M.AddDomainIntegrator(new MassIntegrator());
+   M.Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
+   M.FormSystemMatrix(ess_tdof_list, Mmat);

   M_solver.iterative_mode = false;
-   M_solver.SetRelTol(rel_tol);
+   M_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
   M_solver.SetAbsTol(0.0);
   M_solver.SetMaxIter(100);
   M_solver.SetPrintLevel(0);
@@ -442,97 +518,118 @@ ConductionOperator::ConductionOperator(ParFiniteElementSpace &f, double al,
   M_solver.SetPreconditioner(M_prec);
   M_solver.SetOperator(Mmat);

-   alpha = al;
-   kappa = kap;
-
   T_solver.iterative_mode = false;
-   T_solver.SetRelTol(rel_tol);
+   T_solver.SetRelTol(rel_tol); // will be overwritten with SUNDIALS integrators
   T_solver.SetAbsTol(0.0);
   T_solver.SetMaxIter(100);
   T_solver.SetPrintLevel(0);
   T_solver.SetPreconditioner(T_prec);

-   SetParameters(u);
+   SetConductionTensor(u);
 }

-void ConductionOperator::Mult(const Vector &u, Vector &du_dt) const
-{
-   // Compute:
-   //    du_dt = M^{-1}*-K(u)
-   // for du_dt
-   Kmat.Mult(u, z);
-   z.Neg(); // z = -z
-   M_solver.Mult(z, du_dt);
-}
-
-void ConductionOperator::ImplicitSolve(const double dt,
-                                       const Vector &u, Vector &du_dt)
-{
-   // Solve the equation:
-   //    du_dt = M^{-1}*[-K(u + dt*du_dt)]
-   // for du_dt
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, dt, Kmat);
-   T_solver.SetOperator(*T);
-   Kmat.Mult(u, z);
-   z.Neg();
-   T_solver.Mult(z, du_dt);
-}
-
-int ConductionOperator::SUNImplicitSetup(const Vector &x,
-                                         const Vector &fx, int jok, int *jcur,
-                                         double gamma)
-{
-   // Setup the ODE Jacobian T = M + gamma K.
-   if (T) { delete T; }
-   T = Add(1.0, Mmat, gamma, Kmat);
-   T_solver.SetOperator(*T);
-   *jcur = 1;
-   return (0);
-}
-
-int ConductionOperator::SUNImplicitSolve(const Vector &b, Vector &x, double tol)
-{
-   // Solve the system A x = z => (M - gamma K) x = M b.
-   Mmat.Mult(b, z);
-   T_solver.Mult(z, x);
-   return (0);
-}
-
-void ConductionOperator::SetParameters(const Vector &u)
+void ConductionOperator::SetConductionTensor(const Vector &u)
 {
+   // Compute K(u_n).
   ParGridFunction u_alpha_gf(&fespace);
   u_alpha_gf.SetFromTrueDofs(u);
   for (int i = 0; i < u_alpha_gf.Size(); i++)
   {
      u_alpha_gf(i) = kappa + alpha*u_alpha_gf(i);
   }
-
-   delete K;
-   K = new ParBilinearForm(&fespace);
-
   GridFunctionCoefficient u_coeff(&u_alpha_gf);

+   K = std::make_unique<ParBilinearForm>(&fespace);
   K->AddDomainIntegrator(new DiffusionIntegrator(u_coeff));
-   K->Assemble(0); // keep sparsity pattern of M and K the same
+   K->Assemble(0); // keep zeros to keep sparsity pattern of M and K the same
   K->FormSystemMatrix(ess_tdof_list, Kmat);
 }

-ConductionOperator::~ConductionOperator()
+void ConductionOperator::ExplicitMult(const Vector &u, Vector &v) const
 {
-   delete T;
-   delete M;
-   delete K;
+   // Compute - K(u_n) u.
+   Kmat.Mult(u, v);
+   v.Neg();
 }

-double InitialTemperature(const Vector &x)
+void ConductionOperator::Mult(const Vector &u, Vector &k) const
 {
-   if (x.Norml2() < 0.5)
+   // Compute - inv(M) K(u_n) u.
+   ExplicitMult(u, z);
+   M_solver.Mult(z, k);
+}
+
+void ConductionOperator::ImplicitSolve(const real_t gam, const Vector &u,
+                                       Vector &k)
+{
+   // Solve for k in M k = - K(u_n) [u + gam*k].
+   ExplicitMult(u, z);
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   T_solver.Mult(z, k);
+}
+
+int ConductionOperator::SUNImplicitSetup(const Vector &u, const Vector &fu,
+                                         int jok, int *jcur, real_t gam)
+{
+   // Compute T = M + gamma K(u_n).
+   T = std::unique_ptr<HypreParMatrix>(Add(1.0, Mmat, gam, Kmat));
+   T_solver.SetOperator(*T);
+   *jcur = SUNTRUE; // this should eventually only be set true if K(u) is used
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNImplicitSolve(const Vector &r, Vector &dk,
+                                         real_t tol)
+{
+   // Solve the system [M + gamma K(u_n)] dk = - K(u_n) u - M k.
+   // What value r is providing depends on the ODE expression form:
+   //   EXPLICIT form: r = -inv(M) K(u_n) u - k
+   //   IMPLICIT form: r = -K(u_n) u - M k
+   T_solver.SetRelTol(tol);
+   if (isExplicit())
   {
-      return 2.0;
+      Mmat.Mult(r, z);
+      T_solver.Mult(z, dk);
   }
   else
   {
-      return 1.0;
+      T_solver.Mult(r, dk);
+   }
+   if (T_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
   }
 }
+
+int ConductionOperator::SUNMassSetup()
+{
+   // Do nothing b/c mass solver was setup in constructor.
+   return SUNLS_SUCCESS;
+}
+
+int ConductionOperator::SUNMassSolve(const Vector &b, Vector &x, real_t tol)
+{
+   // Solve the system M x = b.
+   M_solver.SetRelTol(tol);
+   M_solver.Mult(b, x);
+   if (M_solver.GetConverged())
+   {
+      return SUNLS_SUCCESS;
+   }
+   else
+   {
+      return SUNLS_CONV_FAIL;
+   }
+}
+
+int ConductionOperator::SUNMassMult(const Vector &x, Vector &v)
+{
+   // Compute M x.
+   Mmat.Mult(x, v);
+   return SUNLS_SUCCESS;
+}
@@ -1,7 +1,9 @@
 //                                MFEM Example 9
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9
+// Compile with:
+//    make ex9              (GNU make)
+//    make sundials_ex9     (CMake)
 //
 // Sample runs:
 //    ex9 -m ../../data/periodic-segment.mesh -p 0 -r 2 -s 7 -dt 0.005
@@ -1,7 +1,9 @@
 //                       MFEM Example 9 - Parallel Version
 //                             SUNDIALS Modification
 //
-// Compile with: make ex9p
+// Compile with:
+//    make ex9p             (GNU make)
+//    make sundials_ex9p    (CMake)
 //
 // Sample runs:
 //    mpirun -np 4 ex9p -m ../../data/periodic-segment.mesh -p 1 -rp 1 -s 7 -dt 0.0025
@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/sundials/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -100,6 +99,12 @@ ex10-test-seq: ex10
 	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX10_ARGS))
 ex10p-test-par: ex10p
 	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX10P_ARGS))
+# Example 16: test ARKODE with implicit time stepping using mass form
+EX16_COMMON_ARGS := -s 15
+ex16-test-seq: ex16
+	@$(call mfem-test,$<,, $(SERIAL_NAME),$(EX16_COMMON_ARGS))
+ex16p-test-par: ex16p
+	@$(call mfem-test,$<, $(RUN_MPI), $(PARALLEL_NAME),$(EX16_COMMON_ARGS))

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

@@ -12,11 +12,10 @@
 # Use the MFEM build directory
 MFEM_DIR ?= ../..
 MFEM_BUILD_DIR ?= ../..
+MFEM_INSTALL_DIR ?= ../../mfem
 SRC = $(if $(MFEM_DIR:../..=),$(MFEM_DIR)/examples/superlu/,)
-CONFIG_MK = $(MFEM_BUILD_DIR)/config/config.mk
-# Use the MFEM install directory
-# MFEM_INSTALL_DIR = ../../mfem
-# CONFIG_MK = $(MFEM_INSTALL_DIR)/share/mfem/config.mk
+CONFIG_MK = $(or $(wildcard $(MFEM_BUILD_DIR)/config/config.mk),\
+   $(wildcard $(MFEM_INSTALL_DIR)/share/mfem/config.mk))

 MFEM_LIB_FILE = mfem_is_not_built
 -include $(CONFIG_MK)
@@ -112,8 +112,6 @@ set(SRCS
  qinterp/eval_by_vdim.cpp
  qinterp/grad_by_nodes.cpp
  qinterp/grad_by_vdim.cpp
-  qinterp/grad_phys_by_nodes.cpp
-  qinterp/grad_phys_by_vdim.cpp
  qspace.cpp
  quadinterpolator.cpp
  quadinterpolator_face.cpp
@@ -192,6 +190,9 @@ set(HDRS
  hybridization.hpp
  intrules.hpp
  intrules_cut.hpp
+  kernel_dispatch.hpp
+  kernel_reporter.hpp
+  kernels.hpp
  ceed/interface/basis.hpp
  ceed/interface/integrator.hpp
  ceed/interface/interface.hpp
@@ -223,7 +224,6 @@ set(HDRS
  nonlinearform_ext.hpp
  nonlininteg.hpp
  qfunction.hpp
-  qinterp/dispatch.hpp
  qinterp/eval.hpp
  qinterp/grad.hpp
  qspace.hpp
@@ -280,7 +280,7 @@ void BilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
   boundary_face_integs_marker.Append(&bdr_marker);
 }

-void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
+void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
 {
   if (element_matrices)
   {
@@ -289,9 +289,10 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
      return;
   }

+   const FiniteElement &fe = *fes->GetFE(i);
+
   if (domain_integs.Size())
   {
-      const FiniteElement &fe = *fes->GetFE(i);
      ElementTransformation *eltrans = fes->GetElementTransformation(i);
      domain_integs[0]->AssembleElementMatrix(fe, *eltrans, elmat);
      for (int k = 1; k < domain_integs.Size(); k++)
@@ -302,17 +303,18 @@ void BilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
   }
   else
   {
-      fes->GetElementVDofs(i, vdofs);
-      elmat.SetSize(vdofs.Size());
+      const int ndof = fe.GetDof() * fes->GetVDim();
+      elmat.SetSize(ndof);
      elmat = 0.0;
   }
 }

-void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
+   const FiniteElement &be = *fes->GetBE(i);
+
   if (boundary_integs.Size())
   {
-      const FiniteElement &be = *fes->GetBE(i);
      ElementTransformation *eltrans = fes->GetBdrElementTransformation(i);
      boundary_integs[0]->AssembleElementMatrix(be, *eltrans, elmat);
      for (int k = 1; k < boundary_integs.Size(); k++)
@@ -323,8 +325,81 @@ void BilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
   }
   else
   {
-      fes->GetBdrElementVDofs(i, vdofs);
-      elmat.SetSize(vdofs.Size());
+      const int ndof = be.GetDof() * fes->GetVDim();
+      elmat.SetSize(ndof);
+      elmat = 0.0;
+   }
+}
+
+void BilinearForm::ComputeFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *tr;
+   Mesh *mesh = fes -> GetMesh();
+   tr = mesh -> GetFaceElementTransformations (i);
+
+   const FiniteElement *fe1, *fe2;
+   fe1 = fes->GetFE(tr->Elem1No);
+   if (tr->Elem2No >= 0)
+   {
+      fe2 = fes->GetFE(tr->Elem2No);
+   }
+   else
+   {
+      // The fe2 object is really a dummy and not used on the
+      // boundaries, but we can't dereference a NULL pointer, and we don't
+      // want to actually make a fake element.
+      fe2 = fe1;
+   }
+
+   if (interior_face_integs.Size())
+   {
+      interior_face_integs[0] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elmat);
+      for (int k = 1; k < interior_face_integs.Size(); k++)
+      {
+         interior_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      int ndof = fe1->GetDof() * fes->GetVDim();
+      if (tr->Elem2No >= 0)
+      {
+         ndof += fe2->GetDof() * fes->GetVDim();
+      }
+
+      elmat.SetSize(ndof);
+      elmat = 0.0;
+   }
+}
+
+void BilinearForm::ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *tr;
+   Mesh *mesh = fes -> GetMesh();
+   tr = mesh -> GetBdrFaceTransformations (i);
+
+   const FiniteElement *fe1, *fe2;
+
+   fe1 = fes -> GetFE (tr -> Elem1No);
+   // The fe2 object is really a dummy and not used on the boundaries,
+   // but we can't dereference a NULL pointer, and we don't want to
+   // actually make a fake element.
+   fe2 = fe1;
+
+   if (boundary_face_integs.Size())
+   {
+      boundary_face_integs[0] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elmat);
+      for (int k = 1; k < boundary_face_integs.Size(); k++)
+      {
+         boundary_face_integs[k] -> AssembleFaceMatrix (*fe1, *fe2, *tr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      int ndof = fe1->GetDof() * fes->GetVDim();
+      elmat.SetSize(ndof);
      elmat = 0.0;
   }
 }
@@ -1356,32 +1431,50 @@ void MixedBilinearForm::GetBlocks(Array2D<SparseMatrix *> &blocks) const
   mat->GetBlocks(blocks);
 }

-void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi)
+void MixedBilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi)
 {
-   domain_integs.Append (bfi);
+   domain_integs.Append(bfi);
   domain_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }

-void MixedBilinearForm::AddDomainIntegrator (BilinearFormIntegrator * bfi,
-                                             Array<int> &elem_marker)
+void MixedBilinearForm::AddDomainIntegrator(BilinearFormIntegrator *bfi,
+                                            Array<int> &elem_marker)
 {
-   domain_integs.Append (bfi);
+   domain_integs.Append(bfi);
   domain_integs_marker.Append(&elem_marker);
 }

-void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi)
+void MixedBilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi)
 {
-   boundary_integs.Append (bfi);
+   boundary_integs.Append(bfi);
   boundary_integs_marker.Append(NULL); // NULL marker means apply everywhere
 }

-void MixedBilinearForm::AddBoundaryIntegrator (BilinearFormIntegrator * bfi,
-                                               Array<int> &bdr_marker)
+void MixedBilinearForm::AddBoundaryIntegrator(BilinearFormIntegrator *bfi,
+                                              Array<int> &bdr_marker)
 {
-   boundary_integs.Append (bfi);
+   boundary_integs.Append(bfi);
   boundary_integs_marker.Append(&bdr_marker);
 }

+void MixedBilinearForm::AddInteriorFaceIntegrator(BilinearFormIntegrator *bfi)
+{
+   interior_face_integs.Append(bfi);
+}
+
+void MixedBilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi)
+{
+   boundary_face_integs.Append(bfi);
+   boundary_face_integs_marker.Append(NULL); // NULL marker means apply everywhere
+}
+
+void MixedBilinearForm::AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
+                                             Array<int> &bdr_marker)
+{
+   boundary_face_integs.Append(bfi);
+   boundary_face_integs_marker.Append(&bdr_marker);
+}
+
 void MixedBilinearForm::AddTraceFaceIntegrator (BilinearFormIntegrator * bfi)
 {
   trace_face_integs.Append (bfi);
@@ -1514,6 +1607,108 @@ void MixedBilinearForm::Assemble(int skip_zeros)
      }
   }

+   if (interior_face_integs.Size())
+   {
+      FaceElementTransformations *ftr;
+      Array<int> trial_vdofs2, test_vdofs2;
+      const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
+
+      int nfaces = mesh->GetNumFaces();
+      for (int i = 0; i < nfaces; i++)
+      {
+         ftr = mesh->GetInteriorFaceTransformations(i);
+         if (ftr != NULL)
+         {
+            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
+            trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
+            test_fe1 = test_fes->GetFE(ftr->Elem1No);
+            if (ftr->Elem2No >= 0)
+            {
+               trial_fes->GetElementVDofs(ftr->Elem2No, trial_vdofs2);
+               test_fes->GetElementVDofs(ftr->Elem2No, test_vdofs2);
+               trial_vdofs.Append(trial_vdofs2);
+               test_vdofs.Append(test_vdofs2);
+               trial_fe2 = trial_fes->GetFE(ftr->Elem2No);
+               test_fe2 = test_fes->GetFE(ftr->Elem2No);
+            }
+            else
+            {
+               // The test_fe2 object is really a dummy and not used on the
+               // boundaries, but we can't dereference a NULL pointer, and we don't
+               // want to actually make a fake element.
+               trial_fe2 = trial_fe1;
+               test_fe2 = test_fe1;
+            }
+            for (int k = 0; k < interior_face_integs.Size(); k++)
+            {
+               interior_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                           *test_fe2,
+                                                           *ftr, elemmat);
+               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
+            }
+         }
+      }
+   }
+
+   if (boundary_face_integs.Size())
+   {
+      FaceElementTransformations *ftr;
+      Array<int> tr_vdofs2, te_vdofs2;
+      const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
+
+      // Which boundary attributes need to be processed?
+      Array<int> bdr_attr_marker(mesh->bdr_attributes.Size() ?
+                                 mesh->bdr_attributes.Max() : 0);
+      bdr_attr_marker = 0;
+      for (int k = 0; k < boundary_face_integs.Size(); k++)
+      {
+         if (boundary_face_integs_marker[k] == NULL)
+         {
+            bdr_attr_marker = 1;
+            break;
+         }
+         Array<int> &bdr_marker = *boundary_face_integs_marker[k];
+         MFEM_ASSERT(bdr_marker.Size() == bdr_attr_marker.Size(),
+                     "invalid boundary marker for boundary face integrator #"
+                     << k << ", counting from zero");
+         for (int i = 0; i < bdr_attr_marker.Size(); i++)
+         {
+            bdr_attr_marker[i] |= bdr_marker[i];
+         }
+      }
+
+      for (int i = 0; i < trial_fes -> GetNBE(); i++)
+      {
+         const int bdr_attr = mesh->GetBdrAttribute(i);
+         if (bdr_attr_marker[bdr_attr-1] == 0) { continue; }
+
+         ftr = mesh -> GetBdrFaceTransformations (i);
+         if (ftr != NULL)
+         {
+            trial_fes->GetElementVDofs(ftr->Elem1No, trial_vdofs);
+            test_fes->GetElementVDofs(ftr->Elem1No, test_vdofs);
+            trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
+            test_fe1 = test_fes->GetFE(ftr->Elem1No);
+            // The test_fe2 object is really a dummy and not used on the
+            // boundaries, but we can't dereference a NULL pointer, and we don't
+            // want to actually make a fake element.
+            trial_fe2 = trial_fe1;
+            test_fe2 = test_fe1;
+            for (int k = 0; k < boundary_face_integs.Size(); k++)
+            {
+               if (boundary_face_integs_marker[k] &&
+                   (*boundary_face_integs_marker[k])[bdr_attr-1] == 0) { continue; }
+
+               boundary_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                           *test_fe2,
+                                                           *ftr, elemmat);
+               mat->AddSubMatrix(test_vdofs, trial_vdofs, elemmat, skip_zeros);
+            }
+         }
+      }
+   }
+
   if (trace_face_integs.Size())
   {
      FaceElementTransformations *ftr;
@@ -1692,12 +1887,13 @@ void MixedBilinearForm::ConformingAssemble()
 }


-void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
+void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat) const
 {
+   const FiniteElement &trial_fe = *trial_fes->GetFE(i);
+   const FiniteElement &test_fe = *test_fes->GetFE(i);
+
   if (domain_integs.Size())
   {
-      const FiniteElement &trial_fe = *trial_fes->GetFE(i);
-      const FiniteElement &test_fe = *test_fes->GetFE(i);
      ElementTransformation *eltrans = test_fes->GetElementTransformation(i);
      domain_integs[0]->AssembleElementMatrix2(trial_fe, test_fe, *eltrans,
                                               elmat);
@@ -1710,19 +1906,21 @@ void MixedBilinearForm::ComputeElementMatrix(int i, DenseMatrix &elmat)
   }
   else
   {
-      trial_fes->GetElementVDofs(i, trial_vdofs);
-      test_fes->GetElementVDofs(i, test_vdofs);
-      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+      const int tr_dofs = trial_fe.GetDof() * trial_fes->GetVDim();
+      const int te_dofs = test_fe.GetDof() * test_fes->GetVDim();
+
+      elmat.SetSize(te_dofs, tr_dofs);
      elmat = 0.0;
   }
 }

-void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
+void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const
 {
+   const FiniteElement &trial_be = *trial_fes->GetBE(i);
+   const FiniteElement &test_be = *test_fes->GetBE(i);
+
   if (boundary_integs.Size())
   {
-      const FiniteElement &trial_be = *trial_fes->GetBE(i);
-      const FiniteElement &test_be = *test_fes->GetBE(i);
      ElementTransformation *eltrans = test_fes->GetBdrElementTransformation(i);
      boundary_integs[0]->AssembleElementMatrix2(trial_be, test_be, *eltrans,
                                                 elmat);
@@ -1735,9 +1933,191 @@ void MixedBilinearForm::ComputeBdrElementMatrix(int i, DenseMatrix &elmat)
   }
   else
   {
-      trial_fes->GetBdrElementVDofs(i, trial_vdofs);
-      test_fes->GetBdrElementVDofs(i, test_vdofs);
-      elmat.SetSize(test_vdofs.Size(), trial_vdofs.Size());
+      const int tr_dofs = trial_be.GetDof() * trial_fes->GetVDim();
+      const int te_dofs = test_be.GetDof() * test_fes->GetVDim();
+
+      elmat.SetSize(te_dofs, tr_dofs);
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetFaceElementTransformations(i);
+   MFEM_ASSERT(ftr, "No associated face transformations.");
+
+   const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
+
+   trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   if (ftr->Elem2No >= 0)
+   {
+      trial_fe2 = trial_fes->GetFE(ftr->Elem2No);
+      test_fe2 = test_fes->GetFE(ftr->Elem2No);
+   }
+   else
+   {
+      // The test_fe2 object is really a dummy and not used on the
+      // boundaries, but we can't dereference a NULL pointer, and we don't
+      // want to actually make a fake element.
+      trial_fe2 = trial_fe1;
+      test_fe2 = test_fe1;
+   }
+
+   if (interior_face_integs.Size())
+   {
+      interior_face_integs[0]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                  *test_fe2,
+                                                  *ftr, elmat);
+      for (int k = 1; k < interior_face_integs.Size(); k++)
+      {
+         interior_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                     *test_fe2,
+                                                     *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      int tr_dofs = trial_fe1->GetDof() * trial_fes->GetVDim();
+      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+      if (ftr->Elem2No >= 0)
+      {
+         tr_dofs += trial_fe2->GetDof() * trial_fes->GetVDim();
+         te_dofs += test_fe2->GetDof() * test_fes->GetVDim();
+      }
+
+      elmat.SetSize(te_dofs, tr_dofs);
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetBdrFaceTransformations(i);
+   MFEM_ASSERT(ftr, "No associated boundary face.");
+
+   const FiniteElement *trial_fe1, *trial_fe2, *test_fe1, *test_fe2;
+
+   trial_fe1 = trial_fes->GetFE(ftr->Elem1No);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   // The test_fe2 object is really a dummy and not used on the
+   // boundaries, but we can't dereference a NULL pointer, and we don't
+   // want to actually make a fake element.
+   trial_fe2 = trial_fe1;
+   test_fe2 = test_fe1;
+
+   if (boundary_face_integs.Size())
+   {
+      boundary_face_integs[0]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                  *test_fe2,
+                                                  *ftr, elmat);
+      for (int k = 1; k < boundary_face_integs.Size(); k++)
+      {
+         boundary_face_integs[k]->AssembleFaceMatrix(*trial_fe1, *test_fe1, *trial_fe2,
+                                                     *test_fe2,
+                                                     *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      const int tr_dofs = trial_fe1->GetDof() * trial_fes->GetVDim();
+      const int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+
+      elmat.SetSize(te_dofs, tr_dofs);
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeTraceFaceMatrix(int i, DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetFaceElementTransformations(i);
+   MFEM_ASSERT(ftr, "No associated face transformation.");
+
+   const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
+
+   trial_face_fe = trial_fes->GetFaceElement(i);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   if (ftr->Elem2No >= 0)
+   {
+      test_fe2 = test_fes->GetFE(ftr->Elem2No);
+   }
+   else
+   {
+      // The test_fe2 object is really a dummy and not used on the
+      // boundaries, but we can't dereference a NULL pointer, and we don't
+      // want to actually make a fake element.
+      test_fe2 = test_fe1;
+   }
+
+   if (trace_face_integs.Size())
+   {
+      trace_face_integs[0]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                               *ftr, elmat);
+      for (int k = 1; k < trace_face_integs.Size(); k++)
+      {
+         trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1, *test_fe2,
+                                                  *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      const int tr_face_dofs = trial_face_fe->GetDof() * trial_fes->GetVDim();
+      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+      if (ftr->Elem2No >= 0)
+      {
+         te_dofs += test_fe2->GetDof() * test_fes->GetVDim();
+      }
+
+      elmat.SetSize(te_dofs, tr_face_dofs);
+      elmat = 0.0;
+   }
+}
+
+void MixedBilinearForm::ComputeBdrTraceFaceMatrix(int i,
+                                                  DenseMatrix &elmat) const
+{
+   FaceElementTransformations *ftr;
+   Mesh *mesh = test_fes -> GetMesh();
+   ftr = mesh->GetBdrFaceTransformations(i);
+   MFEM_ASSERT(ftr, "No associated boundary face.");
+
+   const FiniteElement *trial_face_fe, *test_fe1, *test_fe2;
+   int iface = mesh->GetBdrElementFaceIndex(i);
+   trial_face_fe = trial_fes->GetFaceElement(iface);
+   test_fe1 = test_fes->GetFE(ftr->Elem1No);
+   // The test_fe2 object is really a dummy and not used on the
+   // boundaries, but we can't dereference a NULL pointer, and we don't
+   // want to actually make a fake element.
+   test_fe2 = test_fe1;
+
+   if (boundary_trace_face_integs.Size())
+   {
+      boundary_trace_face_integs[0]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
+                                                        *test_fe2,
+                                                        *ftr, elmat);
+      for (int k = 1; k < boundary_trace_face_integs.Size(); k++)
+      {
+         boundary_trace_face_integs[k]->AssembleFaceMatrix(*trial_face_fe, *test_fe1,
+                                                           *test_fe2,
+                                                           *ftr, elemmat);
+         elmat += elemmat;
+      }
+   }
+   else
+   {
+      const int tr_face_dofs = trial_face_fe->GetDof() * trial_fes->GetVDim();
+      int te_dofs = test_fe1->GetDof() * test_fes->GetVDim();
+
+      elmat.SetSize(te_dofs, tr_face_dofs);
      elmat = 0.0;
   }
 }
@@ -1780,36 +2160,59 @@ void MixedBilinearForm::AssembleBdrElementMatrix(
   mat->AddSubMatrix(test_vdofs_, trial_vdofs_, elmat, skip_zeros);
 }

-void MixedBilinearForm::EliminateTrialDofs (
+void MixedBilinearForm::EliminateTrialEssentialBC(
   const Array<int> &bdr_attr_is_ess, const Vector &sol, Vector &rhs )
 {
-   int i, j, k;
-   Array<int> tr_vdofs, cols_marker (trial_fes -> GetVSize());
-
-   cols_marker = 0;
-   for (i = 0; i < trial_fes -> GetNBE(); i++)
-      if (bdr_attr_is_ess[trial_fes -> GetBdrAttribute (i)-1])
-      {
-         trial_fes -> GetBdrElementVDofs (i, tr_vdofs);
-         for (j = 0; j < tr_vdofs.Size(); j++)
-         {
-            if ( (k = tr_vdofs[j]) < 0 )
-            {
-               k = -1-k;
-            }
-            cols_marker[k] = 1;
-         }
-      }
-   mat -> EliminateCols (cols_marker, &sol, &rhs);
+   Array<int> trial_ess_dofs;
+   trial_fes->GetEssentialVDofs(bdr_attr_is_ess, trial_ess_dofs);
+   mat->EliminateCols(trial_ess_dofs, &sol, &rhs);
 }

-void MixedBilinearForm::EliminateEssentialBCFromTrialDofs (
+void MixedBilinearForm::EliminateTrialEssentialBC(const Array<int>
+                                                  &bdr_attr_is_ess)
+{
+   Array<int> trial_ess_dofs;
+   trial_fes->GetEssentialVDofs(bdr_attr_is_ess, trial_ess_dofs);
+   mat->EliminateCols(trial_ess_dofs);
+}
+
+void MixedBilinearForm::EliminateTrialVDofs(const Array<int> &trial_vdofs_,
+                                            const Vector &sol, Vector &rhs)
+{
+   Array<int> trial_vdofs_marker;
+   FiniteElementSpace::ListToMarker(trial_vdofs_, mat->Width(),
+                                    trial_vdofs_marker);
+   mat->EliminateCols(trial_vdofs_marker, &sol, &rhs);
+}
+
+void MixedBilinearForm::EliminateTrialVDofs(const Array<int> &trial_vdofs_)
+{
+   if (mat_e == NULL)
+   {
+      mat_e = new SparseMatrix(mat->Height(), mat->Width());
+   }
+
+   Array<int> trial_vdofs_marker;
+   FiniteElementSpace::ListToMarker(trial_vdofs_, mat->Width(),
+                                    trial_vdofs_marker);
+   mat->EliminateCols(trial_vdofs_marker, *mat_e);
+   mat_e->Finalize();
+}
+
+void MixedBilinearForm::EliminateTrialVDofsInRHS(const Array<int> &trial_vdofs_,
+                                                 const Vector &x, Vector &b)
+{
+   mat_e->AddMult(x, b, -1.);
+}
+
+void MixedBilinearForm::EliminateEssentialBCFromTrialDofs(
   const Array<int> &marked_vdofs, const Vector &sol, Vector &rhs)
 {
-   mat -> EliminateCols (marked_vdofs, &sol, &rhs);
+   mat->EliminateCols(marked_vdofs, &sol, &rhs);
 }

-void MixedBilinearForm::EliminateTestDofs (const Array<int> &bdr_attr_is_ess)
+void MixedBilinearForm::EliminateTestEssentialBC(const Array<int>
+                                                 &bdr_attr_is_ess)
 {
   int i, j, k;
   Array<int> te_vdofs;
@@ -1829,6 +2232,14 @@ void MixedBilinearForm::EliminateTestDofs (const Array<int> &bdr_attr_is_ess)
      }
 }

+void MixedBilinearForm::EliminateTestVDofs(const Array<int> &test_vdofs_)
+{
+   for (int i=0; i<test_vdofs_.Size(); ++i)
+   {
+      mat->EliminateRow(test_vdofs_[i]);
+   }
+}
+
 void MixedBilinearForm::FormRectangularSystemMatrix(
   const Array<int> &trial_tdof_list,
   const Array<int> &test_tdof_list,
@@ -1865,20 +2276,9 @@ void MixedBilinearForm::FormRectangularSystemMatrix(
      mat = m;
   }

-   Array<int> ess_trial_tdof_marker, ess_test_tdof_marker;
-   FiniteElementSpace::ListToMarker(trial_tdof_list, trial_fes->GetTrueVSize(),
-                                    ess_trial_tdof_marker);
-   FiniteElementSpace::ListToMarker(test_tdof_list, test_fes->GetTrueVSize(),
-                                    ess_test_tdof_marker);
+   EliminateTrialVDofs(trial_tdof_list);
+   EliminateTestVDofs(test_tdof_list);

-   mat_e = new SparseMatrix(mat->Height(), mat->Width());
-   mat->EliminateCols(ess_trial_tdof_marker, *mat_e);
-
-   for (int i=0; i<test_tdof_list.Size(); ++i)
-   {
-      mat->EliminateRow(test_tdof_list[i]);
-   }
-   mat_e->Finalize();
   A.Reset(mat, false);
 }

@@ -1907,7 +2307,7 @@ void MixedBilinearForm::FormRectangularLinearSystem(
                                  A); // Set A = mat_e
   }
   // Eliminate essential BCs with B -= Ab xb
-   mat_e->AddMult(X, B, -1.0);
+   EliminateTrialVDofsInRHS(trial_tdof_list, X, B);

   B.SetSubVector(test_tdof_list, 0.0);
 }
@@ -1933,6 +2333,10 @@ MixedBilinearForm::~MixedBilinearForm()
      for (i = 0; i < domain_integs.Size(); i++) { delete domain_integs[i]; }
      for (i = 0; i < boundary_integs.Size(); i++)
      { delete boundary_integs[i]; }
+      for (i = 0; i < interior_face_integs.Size(); i++)
+      { delete interior_face_integs[i]; }
+      for (i = 0; i < boundary_face_integs.Size(); i++)
+      { delete boundary_face_integs[i]; }
      for (i = 0; i < trace_face_integs.Size(); i++)
      { delete trace_face_integs[i]; }
      for (i = 0; i < boundary_trace_face_integs.Size(); i++)
@@ -119,8 +119,8 @@ protected:
   Array<BilinearFormIntegrator*> boundary_face_integs;
   Array<Array<int>*> boundary_face_integs_marker; ///< Entries are not owned.

-   DenseMatrix elemmat;
-   Array<int>  vdofs;
+   mutable DenseMatrix elemmat;
+   mutable Array<int>  vdofs;

   DenseTensor *element_matrices; ///< Owned.

@@ -294,13 +294,13 @@ public:
   const real_t &operator()(int i, int j) { return (*mat)(i,j); }

   /// Returns a reference to: $ M_{ij} $
-   virtual real_t &Elem(int i, int j);
+   real_t &Elem(int i, int j) override;

   /// Returns constant reference to: $ M_{ij} $
-   virtual const real_t &Elem(int i, int j) const;
+   const real_t &Elem(int i, int j) const override;

   /// Matrix vector multiplication:  $ y = M x $
-   virtual void Mult(const Vector &x, Vector &y) const;
+   void Mult(const Vector &x, Vector &y) const override;

   /** @brief Matrix vector multiplication with the original uneliminated
       matrix.  The original matrix is $ M + M_e $ so we have:
@@ -309,7 +309,7 @@ public:
   { mat->Mult(x, y); mat_e->AddMult(x, y); }

   /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   virtual void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const
+   void AddMult(const Vector &x, Vector &y, const real_t a = 1.0) const override
   { mat -> AddMult (x, y, a); }

   /** @brief Add the original uneliminated matrix vector multiple to a vector.
@@ -319,8 +319,8 @@ public:
   { mat->AddMult(x, y); mat_e->AddMult(x, y); }

   /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
-   virtual void AddMultTranspose(const Vector & x, Vector & y,
-                                 const real_t a = 1.0) const
+   void AddMultTranspose(const Vector & x, Vector & y,
+                         const real_t a = 1.0) const override
   { mat->AddMultTranspose(x, y, a); }

   /** @brief Add the original uneliminated matrix transpose vector
@@ -330,7 +330,7 @@ public:
   { mat->AddMultTranspose(x, y); mat_e->AddMultTranspose(x, y); }

   /// Matrix transpose vector multiplication:  $ y = M^T x $
-   virtual void MultTranspose(const Vector & x, Vector & y) const;
+   void MultTranspose(const Vector & x, Vector & y) const override;

   /// Compute $ y^T M x $
   real_t InnerProduct(const Vector &x, const Vector &y) const
@@ -338,13 +338,13 @@ public:

   /** @brief Returns a pointer to (approximation) of the matrix inverse:
       $ M^{-1} $ (currently returns NULL) */
-   virtual MatrixInverse *Inverse() const;
+   MatrixInverse *Inverse() const override;

   /** @brief Finalizes the matrix initialization if the ::AssemblyLevel is
       AssemblyLevel::LEGACY.
       The matrix that gets finalized is different if you are using static
       condensation or hybridization.*/
-   virtual void Finalize(int skip_zeros = 1);
+   void Finalize(int skip_zeros = 1) override;

   /** @brief Returns a const reference to the sparse matrix:  $ M $
    *
@@ -458,18 +458,18 @@ public:
       conforming prolongation, and |.| denotes the entry-wise absolute value.
       In general, this is just an approximation of the exact diagonal for this
       case. */
-   virtual void AssembleDiagonal(Vector &diag) const;
+   void AssembleDiagonal(Vector &diag) const override;

   /// Get the finite element space prolongation operator.
-   virtual const Operator *GetProlongation() const
+   const Operator *GetProlongation() const override
   { return fes->GetConformingProlongation(); }

   /// Get the finite element space restriction operator
-   virtual const Operator *GetRestriction() const
+   const Operator *GetRestriction() const override
   { return fes->GetConformingRestriction(); }

   /// Get the output finite element space prolongation matrix
-   virtual const Operator *GetOutputProlongation() const
+   const Operator *GetOutputProlongation() const override
   { return GetProlongation(); }

   /** @brief Returns the output fe space restriction matrix, transposed
@@ -477,11 +477,11 @@ public:
       Logically, this is the transpose of GetOutputRestriction, but in
       practice it is convenient to have it in transposed form for
       construction of RAP operators in matrix-free methods. */
-   virtual const Operator *GetOutputRestrictionTranspose() const
+   const Operator *GetOutputRestrictionTranspose() const override
   { return fes->GetRestrictionTransposeOperator(); }

   /// Get the output finite element space restriction matrix
-   virtual const Operator *GetOutputRestriction() const
+   const Operator *GetOutputRestriction() const override
   { return GetRestriction(); }

   /// Compute serial RAP operator and store it in @a A as a SparseMatrix.
@@ -566,7 +566,8 @@ public:
       FormLinearSystem() method to recover the solution as a GridFunction-size
       vector in @a x. Use the same arguments as in the FormLinearSystem() call.
   */
-   virtual void RecoverFEMSolution(const Vector &X, const Vector &b, Vector &x);
+   void RecoverFEMSolution(const Vector &X, const Vector &b,
+                           Vector &x) override;

   /// Compute and store internally all element matrices.
   void ComputeElementMatrices();
@@ -580,10 +581,18 @@ public:
       or the one stored internally by a prior call of ComputeElementMatrices()
       is returned when available.
   */
-   void ComputeElementMatrix(int i, DenseMatrix &elmat);
+   void ComputeElementMatrix(int i, DenseMatrix &elmat) const;

   /// Compute the boundary element matrix of the given boundary element
-   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the face matrix of the given face element
+   void ComputeFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the boundary face matrix of the given boundary element
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const;

   /// Assemble the given element matrix
   /** The element matrix @a elmat is assembled for the element @a i, i.e.
@@ -763,6 +772,14 @@ protected:
   /// Entries are not owned.
   Array<Array<int>*> boundary_integs_marker;

+   /// Interior face integrators.
+   Array<BilinearFormIntegrator*> interior_face_integs;
+
+   /// Boundary face integrators.
+   Array<BilinearFormIntegrator*> boundary_face_integs;
+   /// Entries are not owned.
+   Array<Array<int>*> boundary_face_integs_marker;
+
   /// Trace face (skeleton) integrators.
   Array<BilinearFormIntegrator*> trace_face_integs;

@@ -771,8 +788,8 @@ protected:
   /// Entries are not owned.
   Array<Array<int>*> boundary_trace_face_integs_marker;

-   DenseMatrix elemmat;
-   Array<int>  trial_vdofs, test_vdofs;
+   mutable DenseMatrix elemmat;
+   mutable Array<int>  trial_vdofs, test_vdofs;

 private:
   /// Copy construction is not supported; body is undefined.
@@ -803,32 +820,32 @@ public:
                     MixedBilinearForm *mbf);

   /// Returns a reference to: $ M_{ij} $
-   virtual real_t &Elem(int i, int j);
+   real_t &Elem(int i, int j) override;

   /// Returns a reference to: $ M_{ij} $
-   virtual const real_t &Elem(int i, int j) const;
+   const real_t &Elem(int i, int j) const override;

   /// Matrix multiplication: $ y = M x $
-   virtual void Mult(const Vector & x, Vector & y) const;
+   void Mult(const Vector & x, Vector & y) const override;

   /// Add the matrix vector multiple to a vector:  $ y += a M x $
-   virtual void AddMult(const Vector & x, Vector & y,
-                        const real_t a = 1.0) const;
+   void AddMult(const Vector & x, Vector & y,
+                const real_t a = 1.0) const override;

   /// Matrix transpose vector multiplication:  $ y = M^T x $
-   virtual void MultTranspose(const Vector & x, Vector & y) const;
+   void MultTranspose(const Vector & x, Vector & y) const override;

   /// Add the matrix transpose vector multiplication:  $ y += a M^T x $
-   virtual void AddMultTranspose(const Vector & x, Vector & y,
-                                 const real_t a = 1.0) const;
+   void AddMultTranspose(const Vector & x, Vector & y,
+                         const real_t a = 1.0) const override;

   /** @brief Returns a pointer to (approximation) of the matrix inverse:
       $ M^{-1} $ (currently unimplemented and returns NULL)*/
-   virtual MatrixInverse *Inverse() const;
+   MatrixInverse *Inverse() const override;

   /** @brief Finalizes the matrix initialization if the ::AssemblyLevel is
       AssemblyLevel::LEGACY.*/
-   virtual void Finalize(int skip_zeros = 1);
+   void Finalize(int skip_zeros = 1) override;

   /** @brief Extract the associated matrix as SparseMatrix blocks. The number
       of block rows and columns is given by the vector dimensions (vdim) of the
@@ -839,15 +856,37 @@ public:
   /** This will segfault if the usual sparse mat is not defined
       like when static condensation is being used or AllocMat() has
       not yet been called. */
-   const SparseMatrix &SpMat() const { return *mat; }
+   const SparseMatrix &SpMat() const
+   {
+      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
+      return *mat;
+   }

   /// Returns a reference to the sparse matrix:  $ M $
-   SparseMatrix &SpMat() { return *mat; }
+   SparseMatrix &SpMat()
+   {
+      MFEM_VERIFY(mat, "mat is NULL and can't be dereferenced");
+      return *mat;
+   }

   /**  @brief Nullifies the internal matrix $ M $ and returns a pointer
        to it.  Used for transferring ownership. */
   SparseMatrix *LoseMat() { SparseMatrix *tmp = mat; mat = NULL; return tmp; }

+   /// Returns a const reference to the sparse matrix of eliminated b.c.:  $ M_e $
+   const SparseMatrix &SpMatElim() const
+   {
+      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
+      return *mat_e;
+   }
+
+   /// Returns a reference to the sparse matrix of eliminated b.c.:  $ M_e $
+   SparseMatrix &SpMatElim()
+   {
+      MFEM_VERIFY(mat_e, "mat_e is NULL and can't be dereferenced");
+      return *mat_e;
+   }
+
   /// Adds a domain integrator. Assumes ownership of @a bfi.
   void AddDomainIntegrator(BilinearFormIntegrator *bfi);

@@ -862,6 +901,16 @@ public:
   void AddBoundaryIntegrator(BilinearFormIntegrator * bfi,
                              Array<int> &bdr_marker);

+   /// Adds an interior face integrator. Assumes ownership of @a bfi.
+   void AddInteriorFaceIntegrator(BilinearFormIntegrator *bfi);
+
+   /// Adds a boundary face integrator. Assumes ownership of @a bfi.
+   void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi);
+
+   /// Adds a boundary face integrator. Assumes ownership of @a bfi.
+   void AddBdrFaceIntegrator(BilinearFormIntegrator *bfi,
+                             Array<int> &bdr_marker);
+
   /** @brief Add a trace face integrator. Assumes ownership of @a bfi.

       This type of integrator assembles terms over all faces of the mesh using
@@ -892,6 +941,16 @@ public:
       corresponding pointer (to Array<int>) will be NULL. */
   Array<Array<int>*> *GetBBFI_Marker() { return &boundary_integs_marker; }

+   /// Access all integrators added with AddInteriorFaceIntegrator().
+   Array<BilinearFormIntegrator*> *GetFBFI() { return &interior_face_integs; }
+
+   /// Access all integrators added with AddBdrFaceIntegrator().
+   Array<BilinearFormIntegrator*> *GetBFBFI() { return &boundary_face_integs; }
+   /** @brief Access all boundary markers added with AddBdrFaceIntegrator().
+       If no marker was specified when the integrator was added, the
+       corresponding pointer (to Array<int>) will be NULL. */
+   Array<Array<int>*> *GetBFBFI_Marker() { return &boundary_face_integs_marker; }
+
   /// Access all integrators added with AddTraceFaceIntegrator().
   Array<BilinearFormIntegrator*> *GetTFBFI() { return &trace_face_integs; }

@@ -920,19 +979,19 @@ public:
   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;

   /// Get the input finite element space prolongation matrix
-   virtual const Operator *GetProlongation() const
+   const Operator *GetProlongation() const override
   { return trial_fes->GetProlongationMatrix(); }

   /// Get the input finite element space restriction matrix
-   virtual const Operator *GetRestriction() const
+   const Operator *GetRestriction() const override
   { return trial_fes->GetRestrictionMatrix(); }

   /// Get the test finite element space prolongation matrix
-   virtual const Operator *GetOutputProlongation() const
+   const Operator *GetOutputProlongation() const override
   { return test_fes->GetProlongationMatrix(); }

   /// Get the test finite element space restriction matrix
-   virtual const Operator *GetOutputRestriction() const
+   const Operator *GetOutputRestriction() const override
   { return test_fes->GetRestrictionMatrix(); }

   /** @brief For partially conforming trial and/or test FE spaces, complete the
@@ -944,10 +1003,25 @@ public:
   void ConformingAssemble();

   /// Compute the element matrix of the given element
-   void ComputeElementMatrix(int i, DenseMatrix &elmat);
+   void ComputeElementMatrix(int i, DenseMatrix &elmat) const;

   /// Compute the boundary element matrix of the given boundary element
-   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat);
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrElementMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the trace face matrix of the given face element
+   void ComputeTraceFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the boundary trace face matrix of the given boundary element
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrTraceFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the face matrix of the given face element
+   void ComputeFaceMatrix(int i, DenseMatrix &elmat) const;
+
+   /// Compute the boundary face matrix of the given boundary element
+   /** @note The boundary attribute markers of the integrators are ignored. */
+   void ComputeBdrFaceMatrix(int i, DenseMatrix &elmat) const;

   /// Assemble the given element matrix
   /** The element matrix @a elmat is assembled for the element @a i, i.e.
@@ -989,24 +1063,61 @@ public:
                                 Array<int> &test_vdofs,
                                 int skip_zeros = 1);

-   /// Eliminate essential boundary DOFs from the columns of the system.
+   /// Eliminate essential boundary trial DOFs from the system.
   /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
-       the essential part of the boundary.  All entries in the columns will be
-       set to 0.0 through elimination.*/
-   void EliminateTrialDofs(const Array<int> &bdr_attr_is_ess,
-                           const Vector &sol, Vector &rhs);
+       the essential part of the boundary. */
+   void EliminateTrialEssentialBC(const Array<int> &bdr_attr_is_ess,
+                                  const Vector &sol, Vector &rhs);

-   /// Eliminate the list of DOFs from the columns of the system.
-   /** @a marked_vdofs is the of colunm numbers that will be eliminated.  All
-       entries in the columns will be set to 0.0 through elimination.*/
+   /// Eliminate essential boundary trial DOFs from the system matrix.
+   /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
+       the essential part of the boundary. */
+   void EliminateTrialEssentialBC(const Array<int> &bdr_attr_is_ess);
+
+   /// (DEPRECATED) Eliminate essential boundary trial DOFs from the system.
+   /** @see EliminateTrialEssentialBC() */
+   MFEM_DEPRECATED void EliminateTrialDofs(const Array<int> &bdr_attr_is_ess,
+                                           const Vector &sol, Vector &rhs)
+   { EliminateTrialEssentialBC(bdr_attr_is_ess, sol, rhs); }
+
+   /// Eliminate the given trial @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
+   /** In this case the eliminations are applied to the internal $ M $
+       and @a rhs without storing the elimination matrix $ M_e $. */
+   void EliminateTrialVDofs(const Array<int> &vdofs, const Vector &sol,
+                            Vector &rhs);
+
+   /// Eliminate the given trial @a vdofs, storing the eliminated part internally in $ M_e $.
+   /** This method works in conjunction with EliminateTrialVDofsInRHS() and allows
+       elimination of boundary conditions in multiple right-hand sides. In this
+       method, @a vdofs is a list of DOFs. */
+   void EliminateTrialVDofs(const Array<int> &vdofs);
+
+   /** @brief Use the stored eliminated part of the matrix (see
+       EliminateTrialVDofs(const Array<int> &)) to modify the r.h.s.
+       @a b; @a vdofs is a list of DOFs (non-directional, i.e. >= 0). */
+   void EliminateTrialVDofsInRHS(const Array<int> &vdofs, const Vector &x,
+                                 Vector &b);
+
+   /** @brief Similar to
+      EliminateTrialVDofs(const Array<int> &, const Vector &, Vector &)
+      but here @a ess_dofs is a marker (boolean) array on all vector-dofs
+      (@a ess_dofs[i] < 0 is true). */
   void EliminateEssentialBCFromTrialDofs(const Array<int> &marked_vdofs,
                                          const Vector &sol, Vector &rhs);

-   /// Eliminate essential boundary DOFs from the rows of the system.
+   /// Eliminate essential boundary test DOFs from the system matrix.
   /** The array @a bdr_attr_is_ess marks boundary attributes that constitute
-       the essential part of the boundary.  All entries in the rows will be
-       set to 0.0 through elimination.*/
-   virtual void EliminateTestDofs(const Array<int> &bdr_attr_is_ess);
+       the essential part of the boundary. */
+   void EliminateTestEssentialBC(const Array<int> &bdr_attr_is_ess);
+
+   /// (DEPRECATED) Eliminate essential boundary test DOFs from the system.
+   /** @see EliminateTestEssentialBC() */
+   MFEM_DEPRECATED virtual void EliminateTestDofs(const Array<int>
+                                                  &bdr_attr_is_ess)
+   { EliminateTestEssentialBC(bdr_attr_is_ess); }
+
+   /// Eliminate the given test @a vdofs. NOTE: here, @a vdofs is a list of DOFs.
+   void EliminateTestVDofs(const Array<int> &vdofs);

   /** @brief Return in @a A that is column-constrained.

@@ -1162,7 +1273,7 @@ public:

   /** @brief Get the output finite element space restriction matrix in
       transposed form. */
-   virtual const Operator *GetOutputRestrictionTranspose() const
+   const Operator *GetOutputRestrictionTranspose() const override
   { return test_fes->GetRestrictionTransposeOperator(); }
 };

@@ -37,19 +37,19 @@ protected:
 public:
   BilinearFormExtension(BilinearForm *form);

-   virtual MemoryClass GetMemoryClass() const
+   MemoryClass GetMemoryClass() const override
   { return Device::GetDeviceMemoryClass(); }

   /// Get the finite element space prolongation matrix
-   virtual const Operator *GetProlongation() const;
+   const Operator *GetProlongation() const override;

   /// Get the finite element space restriction matrix
-   virtual const Operator *GetRestriction() const;
+   const Operator *GetRestriction() const override;

   /// Assemble at the level given for the BilinearFormExtension subclass
   virtual void Assemble() = 0;

-   virtual void AssembleDiagonal(Vector &diag) const
+   void AssembleDiagonal(Vector &diag) const override
   {
      MFEM_ABORT("AssembleDiagonal not implemented for this assembly level!");
   }
@@ -83,16 +83,17 @@ protected:
 public:
   PABilinearFormExtension(BilinearForm*);

-   void Assemble();
-   void AssembleDiagonal(Vector &diag) const;
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
+   void Assemble() override;
+   void AssembleDiagonal(Vector &diag) const override;
+   void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                         OperatorHandle &A) override;
   void FormLinearSystem(const Array<int> &ess_tdof_list,
                         Vector &x, Vector &b,
                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
-   void Update();
+                         int copy_interior = 0) override;
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;
+   void Update() override;

 protected:
   void SetupRestrictionOperators(const L2FaceValues m);
@@ -150,9 +151,9 @@ protected:
 public:
   EABilinearFormExtension(BilinearForm *form);

-   void Assemble();
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
+   void Assemble() override;
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;
 };

 /// Data and methods for fully-assembled bilinear forms
@@ -165,18 +166,19 @@ private:
 public:
   FABilinearFormExtension(BilinearForm *form);

-   void Assemble();
+   void Assemble() override;
   void RAP(OperatorHandle &A);
   /** @note Always does `DIAG_ONE` policy to be consistent with
       `Operator::FormConstrainedSystemOperator`. */
   void EliminateBC(const Array<int> &ess_dofs, OperatorHandle &A);
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
+   void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                         OperatorHandle &A) override;
   void FormLinearSystem(const Array<int> &ess_tdof_list,
                         Vector &x, Vector &b,
                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
+                         int copy_interior = 0) override;
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;

   /** DGMult and DGMultTranspose use the extended L-vector to perform the
       computation. */
@@ -199,16 +201,17 @@ protected:
 public:
   MFBilinearFormExtension(BilinearForm *form);

-   void Assemble();
-   void AssembleDiagonal(Vector &diag) const;
-   void FormSystemMatrix(const Array<int> &ess_tdof_list, OperatorHandle &A);
+   void Assemble() override;
+   void AssembleDiagonal(Vector &diag) const override;
+   void FormSystemMatrix(const Array<int> &ess_tdof_list,
+                         OperatorHandle &A) override;
   void FormLinearSystem(const Array<int> &ess_tdof_list,
                         Vector &x, Vector &b,
                         OperatorHandle &A, Vector &X, Vector &B,
-                         int copy_interior = 0);
-   void Mult(const Vector &x, Vector &y) const;
-   void MultTranspose(const Vector &x, Vector &y) const;
-   void Update();
+                         int copy_interior = 0) override;
+   void Mult(const Vector &x, Vector &y) const override;
+   void MultTranspose(const Vector &x, Vector &y) const override;
+   void Update() override;
 };

 /// Class extending the MixedBilinearForm class to support different AssemblyLevels.
@@ -225,20 +228,20 @@ protected:
 public:
   MixedBilinearFormExtension(MixedBilinearForm *form);

-   virtual MemoryClass GetMemoryClass() const
+   MemoryClass GetMemoryClass() const override
   { return Device::GetMemoryClass(); }

   /// Get the finite element space prolongation matrix
-   virtual const Operator *GetProlongation() const;
+   const Operator *GetProlongation() const override;

   /// Get the finite element space restriction matrix
-   virtual const Operator *GetRestriction() const;
+   const Operator *GetRestriction() const override;

   /// Get the output finite element space restriction matrix
-   virtual const Operator *GetOutputProlongation() const;
+   const Operator *GetOutputProlongation() const override;

   /// Get the output finite element space restriction matrix
-   virtual const Operator *GetOutputRestriction() const;
+   const Operator *GetOutputRestriction() const override;

   virtual void Assemble() = 0;
   virtual void FormRectangularSystemOperator(const Array<int> &trial_tdof_list,
@@ -273,7 +276,7 @@ public:
   PAMixedBilinearFormExtension(MixedBilinearForm *form);

   /// Partial assembly of all internal integrators
-   void Assemble();
+   void Assemble() override;
   /**
      @brief Setup OperatorHandle A to contain constrained linear operator

@@ -283,7 +286,7 @@ public:
   */
   void FormRectangularSystemOperator(const Array<int> &trial_tdof_list,
                                      const Array<int> &test_tdof_list,
-                                      OperatorHandle &A);
+                                      OperatorHandle &A) override;
   /**
      Setup OperatorHandle A to contain constrained linear operator and
      eliminate columns corresponding to essential dofs from system,
@@ -292,20 +295,21 @@ public:
   void FormRectangularLinearSystem(const Array<int> &trial_tdof_list,
                                    const Array<int> &test_tdof_list,
                                    Vector &x, Vector &b,
-                                    OperatorHandle &A, Vector &X, Vector &B);
+                                    OperatorHandle &A, Vector &X, Vector &B) override;
   /// y = A*x
-   void Mult(const Vector &x, Vector &y) const;
+   void Mult(const Vector &x, Vector &y) const override;
   /// y += c*A*x
-   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const override;
   /// y = A^T*x
-   void MultTranspose(const Vector &x, Vector &y) const;
+   void MultTranspose(const Vector &x, Vector &y) const override;
   /// y += c*A^T*x
-   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
+   void AddMultTranspose(const Vector &x, Vector &y,
+                         const real_t c=1.0) const override;
   /// Assemble the diagonal of ADA^T for a diagonal vector D.
-   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const;
+   void AssembleDiagonal_ADAt(const Vector &D, Vector &diag) const override;

   /// Update internals for when a new MixedBilinearForm is given to this class
-   void Update();
+   void Update() override;
 };


@@ -322,16 +326,17 @@ public:
   PADiscreteLinearOperatorExtension(DiscreteLinearOperator *linop);

   /// Partial assembly of all internal integrators
-   void Assemble();
+   void Assemble() override;

-   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const;
+   void AddMult(const Vector &x, Vector &y, const real_t c=1.0) const override;

-   void AddMultTranspose(const Vector &x, Vector &y, const real_t c=1.0) const;
+   void AddMultTranspose(const Vector &x, Vector &y,
+                         const real_t c=1.0) const override;

   void FormRectangularSystemOperator(const Array<int>&, const Array<int>&,
-                                      OperatorHandle& A);
+                                      OperatorHandle& A) override;

-   const Operator * GetOutputRestrictionTranspose() const;
+   const Operator * GetOutputRestrictionTranspose() const override;

 private:
   Vector test_multiplicity;
@@ -170,6 +170,16 @@ void BilinearFormIntegrator::AssembleFaceMatrix(
              "   is not implemented for this class.");
 }

+void BilinearFormIntegrator::AssembleFaceMatrix(
+   const FiniteElement &trial_fe1, const FiniteElement &test_fe1,
+   const FiniteElement &trial_fe2, const FiniteElement &test_fe2,
+   FaceElementTransformations &Trans,
+   DenseMatrix &elmat)
+{
+   MFEM_ABORT("AssembleFaceMatrix (mixed form) is not implemented for this"
+              " Integrator class.");
+}
+
 void BilinearFormIntegrator::AssembleFaceMatrix(
   const FiniteElement &trial_face_fe, const FiniteElement &test_fe1,
   const FiniteElement &test_fe2, FaceElementTransformations &Trans,
@@ -223,28 +233,38 @@ void TransposeIntegrator::SetIntRule(const IntegrationRule *ir)
   bfi->SetIntRule(ir);
 }

-void TransposeIntegrator::AssembleElementMatrix (
+void TransposeIntegrator::AssembleElementMatrix(
   const FiniteElement &el, ElementTransformation &Trans, DenseMatrix &elmat)
 {
-   bfi -> AssembleElementMatrix (el, Trans, bfi_elmat);
+   bfi->AssembleElementMatrix(el, Trans, bfi_elmat);
   // elmat = bfi_elmat^t
   elmat.Transpose (bfi_elmat);
 }

-void TransposeIntegrator::AssembleElementMatrix2 (
+void TransposeIntegrator::AssembleElementMatrix2(
   const FiniteElement &trial_fe, const FiniteElement &test_fe,
   ElementTransformation &Trans, DenseMatrix &elmat)
 {
-   bfi -> AssembleElementMatrix2 (test_fe, trial_fe, Trans, bfi_elmat);
+   bfi->AssembleElementMatrix2(test_fe, trial_fe, Trans, bfi_elmat);
   // elmat = bfi_elmat^t
   elmat.Transpose (bfi_elmat);
 }

-void TransposeIntegrator::AssembleFaceMatrix (
+void TransposeIntegrator::AssembleFaceMatrix(
   const FiniteElement &el1, const FiniteElement &el2,
   FaceElementTransformations &Trans, DenseMatrix &elmat)
 {
-   bfi -> AssembleFaceMatrix (el1, el2, Trans, bfi_elmat);
+   bfi->AssembleFaceMatrix(el1, el2, Trans, bfi_elmat);
+   // elmat = bfi_elmat^t
+   elmat.Transpose (bfi_elmat);
+}
+
+void TransposeIntegrator::AssembleFaceMatrix(
+   const FiniteElement &tr_el1, const FiniteElement &te_el1,
+   const FiniteElement &tr_el2, const FiniteElement &te_el2,
+   FaceElementTransformations &Trans, DenseMatrix &elmat)
+{
+   bfi->AssembleFaceMatrix(te_el1, tr_el1, te_el2, tr_el2, Trans, bfi_elmat);
   // elmat = bfi_elmat^t
   elmat.Transpose (bfi_elmat);
 }
@@ -1222,7 +1242,8 @@ real_t DiffusionIntegrator::ComputeFluxEnergy
   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);
-      fluxelem.CalcShape(ip, shape);
+      Trans.SetIntPoint(&ip);
+      fluxelem.CalcPhysShape(Trans, shape);

      pointflux = 0.0;
      for (int k = 0; k < spaceDim; k++)
@@ -1233,7 +1254,6 @@ real_t DiffusionIntegrator::ComputeFluxEnergy
         }
      }

-      Trans.SetIntPoint(&ip);
      real_t w = Trans.Weight() * ip.weight;

      if (MQ)
@@ -1410,9 +1430,7 @@ void BoundaryMassIntegrator::AssembleFaceMatrix(
      // Set the integration point in the face and the neighboring element
      Trans.SetAllIntPoints(&ip);

-      // Access the neighboring element's integration point
-      const IntegrationPoint &eip = Trans.GetElement1IntPoint();
-      el1.CalcShape(eip, shape);
+      el1.CalcPhysShape(*Trans.Elem1, shape);

      w = Trans.Weight() * ip.weight;
      if (Q)
@@ -1582,9 +1600,9 @@ void VectorMassIntegrator::AssembleElementMatrix
   for (int s = 0; s < ir->GetNPoints(); s++)
   {
      const IntegrationPoint &ip = ir->IntPoint(s);
-      el.CalcShape(ip, shape);
-
      Trans.SetIntPoint (&ip);
+      el.CalcPhysShape(Trans, shape);
+
      norm = ip.weight * Trans.Weight();

      MultVVt(shape, partelmat);
@@ -1666,10 +1684,10 @@ void VectorMassIntegrator::AssembleElementMatrix2(
   for (int s = 0; s < ir->GetNPoints(); s++)
   {
      const IntegrationPoint &ip = ir->IntPoint(s);
-      trial_fe.CalcShape(ip, shape);
-      test_fe.CalcShape(ip, te_shape);
-
      Trans.SetIntPoint(&ip);
+      trial_fe.CalcPhysShape(Trans, shape);
+      test_fe.CalcPhysShape(Trans, te_shape);
+
      norm = ip.weight * Trans.Weight();

      MultVWt(te_shape, shape, partelmat);
@@ -1897,12 +1915,12 @@ void VectorFECurlIntegrator::AssembleElementMatrix2(
         if ( trial_fe.GetMapType() == mfem::FiniteElement::H_CURL )
         {
            trial_fe.CalcCurlShape(ip, curlshapeTrial_dFT);
-            test_fe.CalcShape(ip, shapeTest);
+            test_fe.CalcPhysShape(Trans, shapeTest);
         }
         else
         {
            test_fe.CalcCurlShape(ip, curlshapeTrial_dFT);
-            trial_fe.CalcShape(ip, shapeTest);
+            trial_fe.CalcPhysShape(Trans, shapeTest);
         }
      }

@@ -1925,6 +1943,89 @@ void VectorFECurlIntegrator::AssembleElementMatrix2(
   }
 }

+void VectorFEBoundaryFluxIntegrator::AssembleElementMatrix(
+   const FiniteElement &el, ElementTransformation &Tr,
+   DenseMatrix &elmat)
+{
+   int nd = el.GetDof();
+   real_t w;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape;
+#endif
+   elmat.SetSize(nd);
+   shape.SetSize(nd);
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int intorder = 2*el.GetOrder() + Tr.OrderW();  // <----------
+      ir = &IntRules.Get(el.GetGeomType(), intorder);
+   }
+
+   elmat = 0.0;
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+      el.CalcShape(ip, shape);
+
+      Tr.SetIntPoint (&ip);
+      w = ip.weight / Tr.Weight();
+
+      if (Q)
+      {
+         w *= Q->Eval(Tr, ip);
+      }
+
+      AddMult_a_VVt(w, shape, elmat);
+   }
+}
+
+void VectorFEBoundaryFluxIntegrator::AssembleElementMatrix2(
+   const FiniteElement &trial_fe,
+   const FiniteElement &test_fe,
+   ElementTransformation &Tr,
+   DenseMatrix &elmat)
+{
+   int tr_nd = trial_fe.GetDof();
+   int te_nd = test_fe.GetDof();
+   real_t w;
+
+#ifdef MFEM_THREAD_SAFE
+   Vector shape, te_shape;
+#endif
+   elmat.SetSize(te_nd, tr_nd);
+   shape.SetSize(tr_nd);
+   te_shape.SetSize(te_nd);
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order = trial_fe.GetOrder() + test_fe.GetOrder() + Tr.OrderW();
+
+      ir = &IntRules.Get(trial_fe.GetGeomType(), order);
+   }
+
+   elmat = 0.0;
+   for (int i = 0; i < ir->GetNPoints(); i++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(i);
+      trial_fe.CalcShape(ip, shape);
+      test_fe.CalcShape(ip, te_shape);
+
+      Tr.SetIntPoint (&ip);
+      w = ip.weight / Tr.Weight();
+
+      if (Q)
+      {
+         w *= Q->Eval(Tr, ip);
+      }
+
+      te_shape *= w;
+      AddMultVWt(te_shape, shape, elmat);
+   }
+}
+
 void DerivativeIntegrator::AssembleElementMatrix2 (
   const FiniteElement &trial_fe,
   const FiniteElement &test_fe,
@@ -1981,7 +2082,7 @@ void DerivativeIntegrator::AssembleElementMatrix2 (
      det = Trans.Weight();
      Mult (dshape, invdfdx, dshapedxt);

-      test_fe.CalcShape(ip, shape);
+      test_fe.CalcPhysShape(Trans, shape);

      for (l = 0; l < trial_nd; l++)
      {
@@ -2566,7 +2667,7 @@ void VectorFEMassIntegrator::AssembleElementMatrix2(
         Trans.SetIntPoint (&ip);

         trial_fe.CalcVShape(Trans, trial_vshape);
-         test_fe.CalcShape(ip, shape);
+         test_fe.CalcPhysShape(Trans, shape);

         w = ip.weight * Trans.Weight();
         if (DQ)
@@ -2726,11 +2827,11 @@ void VectorDivergenceIntegrator::AssembleElementMatrix2(
   for (int i = 0; i < ir -> GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);
+      Trans.SetIntPoint (&ip);

      trial_fe.CalcDShape (ip, dshape);
-      test_fe.CalcShape (ip, shape);
+      test_fe.CalcPhysShape (Trans, shape);

-      Trans.SetIntPoint (&ip);
      CalcAdjugate(Trans.Jacobian(), Jadj);

      Mult (dshape, Jadj, gshape);
@@ -3231,11 +3332,11 @@ real_t ElasticityIntegrator::ComputeFluxEnergy(const FiniteElement &fluxelem,
   for (int i = 0; i < ir->GetNPoints(); i++)
   {
      const IntegrationPoint &ip = ir->IntPoint(i);
-      fluxelem.CalcShape(ip, shape);
+      Trans.SetIntPoint(&ip);
+      fluxelem.CalcPhysShape(Trans, shape);

      flux_mat.MultTranspose(shape, pointstress);

-      Trans.SetIntPoint(&ip);
      real_t w = Trans.Weight() * ip.weight;

      M = mu->Eval(Trans, ip);
@@ -3342,7 +3443,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();

-      el1.CalcShape(eip1, shape1);
+      el1.CalcPhysShape(*Trans.Elem1, shape1);

      u->Eval(vu, *Trans.Elem1, eip1);

@@ -3389,7 +3490,7 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,

      if (ndof2)
      {
-         el2.CalcShape(eip2, shape2);
+         el2.CalcPhysShape(*Trans.Elem2, shape2);

         if (w != 0.0)
            for (int i = 0; i < ndof2; i++)
@@ -3417,6 +3518,150 @@ void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &el1,
   }
 }

+void DGTraceIntegrator::AssembleFaceMatrix(const FiniteElement &trial_fe1,
+                                           const FiniteElement &test_fe1,
+                                           const FiniteElement &trial_fe2,
+                                           const FiniteElement &test_fe2,
+                                           FaceElementTransformations &Trans,
+                                           DenseMatrix &elmat)
+{
+   int tr_ndof1, te_ndof1, tr_ndof2, te_ndof2;
+
+   real_t un, a, b, w;
+
+   dim = test_fe1.GetDim();
+   tr_ndof1 = trial_fe1.GetDof();
+   te_ndof1 = test_fe1.GetDof();
+   Vector vu(dim), nor(dim);
+
+   if (Trans.Elem2No >= 0)
+   {
+      tr_ndof2 = trial_fe2.GetDof();
+      te_ndof2 = test_fe2.GetDof();
+   }
+   else
+   {
+      tr_ndof2 = 0;
+      te_ndof2 = 0;
+   }
+
+   tr_shape1.SetSize(tr_ndof1);
+   te_shape1.SetSize(te_ndof1);
+   tr_shape2.SetSize(tr_ndof2);
+   te_shape2.SetSize(te_ndof2);
+   elmat.SetSize(te_ndof1 + te_ndof2, tr_ndof1 + tr_ndof2);
+   elmat = 0.0;
+
+   const IntegrationRule *ir = IntRule;
+   if (ir == NULL)
+   {
+      int order;
+      // Assuming order(u)==order(mesh)
+      if (Trans.Elem2No >= 0)
+         order = (min(Trans.Elem1->OrderW(), Trans.Elem2->OrderW()) +
+                  max(trial_fe1.GetOrder(), trial_fe2.GetOrder()) +
+                  max(test_fe1.GetOrder(), test_fe2.GetOrder()));
+      else
+      {
+         order = Trans.Elem1->OrderW() + trial_fe1.GetOrder() + test_fe1.GetOrder();
+      }
+      if (trial_fe1.Space() == FunctionSpace::Pk)
+      {
+         order++;
+      }
+      ir = &IntRules.Get(Trans.FaceGeom, order);
+   }
+
+   for (int p = 0; p < ir->GetNPoints(); p++)
+   {
+      const IntegrationPoint &ip = ir->IntPoint(p);
+      IntegrationPoint eip1, eip2;
+      Trans.Loc1.Transform(ip, eip1);
+      Trans.Elem1->SetIntPoint(&eip1);
+      if (tr_ndof2 && te_ndof2)
+      {
+         Trans.Loc2.Transform(ip, eip2);
+         Trans.Elem2->SetIntPoint(&eip2);
+      }
+      trial_fe1.CalcPhysShape(*Trans.Elem1, tr_shape1);
+      test_fe1.CalcPhysShape(*Trans.Elem1, te_shape1);
+
+      Trans.Face->SetIntPoint(&ip);
+
+      u->Eval(vu, *Trans.Elem1, eip1);
+
+      if (dim == 1)
+      {
+         nor(0) = 2*eip1.x - 1.0;
+      }
+      else
+      {
+         CalcOrtho(Trans.Face->Jacobian(), nor);
+      }
+
+      un = vu * nor;
+      a = 0.5 * alpha * un;
+      b = beta * fabs(un);
+      // note: if |alpha/2|==|beta| then |a|==|b|, i.e. (a==b) or (a==-b)
+      //       and therefore two blocks in the element matrix contribution
+      //       (from the current quadrature point) are 0
+
+      if (rho)
+      {
+         real_t rho_p;
+         if (un >= 0.0 && tr_ndof2 && te_ndof2)
+         {
+            Trans.Elem2->SetIntPoint(&eip2);
+            rho_p = rho->Eval(*Trans.Elem2, eip2);
+         }
+         else
+         {
+            rho_p = rho->Eval(*Trans.Elem1, eip1);
+         }
+         a *= rho_p;
+         b *= rho_p;
+      }
+
+      w = ip.weight * (a+b);
+      if (w != 0.0)
+      {
+         for (int i = 0; i < te_ndof1; i++)
+            for (int j = 0; j < tr_ndof1; j++)
+            {
+               elmat(i, j) += w * te_shape1(i) * tr_shape1(j);
+            }
+      }
+
+      if (tr_ndof2 && te_ndof2)
+      {
+         trial_fe2.CalcPhysShape(*Trans.Elem2, tr_shape2);
+         test_fe2.CalcPhysShape(*Trans.Elem2, te_shape2);
+
+         if (w != 0.0)
+            for (int i = 0; i < te_ndof2; i++)
+               for (int j = 0; j < tr_ndof1; j++)
+               {
+                  elmat(te_ndof1+i, j) -= w * te_shape2(i) * tr_shape1(j);
+               }
+
+         w = ip.weight * (b-a);
+         if (w != 0.0)
+         {
+            for (int i = 0; i < te_ndof2; i++)
+               for (int j = 0; j < tr_ndof2; j++)
+               {
+                  elmat(te_ndof1+i, tr_ndof1+j) += w * te_shape2(i) * tr_shape2(j);
+               }
+
+            for (int i = 0; i < te_ndof1; i++)
+               for (int j = 0; j < tr_ndof2; j++)
+               {
+                  elmat(i, tr_ndof1+j) -= w * te_shape1(i) * tr_shape2(j);
+               }
+         }
+      }
+   }
+}

 const IntegrationRule &DGTraceIntegrator::GetRule(
   Geometry::Type geom, int order, FaceElementTransformations &T)
@@ -3939,19 +4184,14 @@ void TraceJumpIntegrator::AssembleFaceMatrix(
      // Set the integration point in the face and the neighboring elements
      Trans.SetAllIntPoints(&ip);

-      // Access the neighboring elements' integration points
-      // Note: eip2 will only contain valid data if Elem2 exists
-      const IntegrationPoint &eip1 = Trans.GetElement1IntPoint();
-      const IntegrationPoint &eip2 = Trans.GetElement2IntPoint();
-
      // Trace finite element shape function
      trial_face_fe.CalcShape(ip, face_shape);
      // Side 1 finite element shape function
-      test_fe1.CalcShape(eip1, shape1);
+      test_fe1.CalcPhysShape(*Trans.Elem1, shape1);
      if (ndof2)
      {
         // Side 2 finite element shape function
-         test_fe2.CalcShape(eip2, shape2);
+         test_fe2.CalcPhysShape(*Trans.Elem2, shape2);
      }
      w = ip.weight;
      if (trial_face_fe.GetMapType() == FiniteElement::VALUE)
@@ -4314,8 +4554,8 @@ struct ShapeCoefficient : public VectorCoefficient
      : VectorCoefficient(fe_.GetDof()), Q(q), fe(fe_) { }

   using VectorCoefficient::Eval;
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   {
      V.SetSize(vdim);
      fe.CalcPhysShape(T, V);
@@ -4357,8 +4597,8 @@ ScalarVectorProductInterpolator::AssembleElementMatrix2(
      VShapeCoefficient(Coefficient &q, const FiniteElement &fe_, int sdim)
         : MatrixCoefficient(fe_.GetDof(), sdim), Q(q), fe(fe_) { }

-      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                        const IntegrationPoint &ip)
+      void Eval(DenseMatrix &M, ElementTransformation &T,
+                const IntegrationPoint &ip) override
      {
         M.SetSize(height, width);
         fe.CalcPhysVShape(T, M);
@@ -4394,8 +4634,8 @@ VectorScalarProductInterpolator::AssembleElementMatrix2(
         : MatrixCoefficient(fe_.GetDof(), vq.GetVDim()), VQ(vq), fe(fe_),
           vc(width), shape(height) { }

-      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                        const IntegrationPoint &ip)
+      void Eval(DenseMatrix &M, ElementTransformation &T,
+                const IntegrationPoint &ip) override
      {
         M.SetSize(height, width);
         VQ.Eval(vc, T, ip);
@@ -4434,8 +4674,8 @@ ScalarCrossProductInterpolator::AssembleElementMatrix2(
           vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }

      using VectorCoefficient::Eval;
-      virtual void Eval(Vector &V, ElementTransformation &T,
-                        const IntegrationPoint &ip)
+      void Eval(Vector &V, ElementTransformation &T,
+                const IntegrationPoint &ip) override
      {
         V.SetSize(vdim);
         VQ.Eval(vc, T, ip);
@@ -4478,8 +4718,8 @@ VectorCrossProductInterpolator::AssembleElementMatrix2(
         MFEM_ASSERT(width == 3, "");
      }

-      virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                        const IntegrationPoint &ip)
+      void Eval(DenseMatrix &M, ElementTransformation &T,
+                const IntegrationPoint &ip) override
      {
         M.SetSize(height, width);
         VQ.Eval(vc, T, ip);
@@ -4527,8 +4767,8 @@ struct VDotVShapeCoefficient : public VectorCoefficient
        vshape(vdim, vq.GetVDim()), vc(vq.GetVDim()) { }

   using VectorCoefficient::Eval;
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   {
      V.SetSize(vdim);
      VQ.Eval(vc, T, ip);
@@ -90,12 +90,12 @@ public:
   explicit ConstantCoefficient(real_t c = 1.0) { constant=c; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   { return (constant); }

   /// Fill the QuadratureFunction @a qf with the constant value.
-   void Project(QuadratureFunction &qf);
+   void Project(QuadratureFunction &qf) override;
 };

 /** @brief A piecewise constant coefficient with the constants keyed
@@ -130,8 +130,8 @@ public:
   int GetNConst() { return constants.Size(); }

   /// Evaluate the coefficient.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /** @brief A piecewise coefficient with the pieces keyed off the element
@@ -195,7 +195,7 @@ public:
   { InitMap(attr, coefs); }

   /// Set the time for time dependent coefficients
-   virtual void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Replace a set of coefficients
   void UpdateCoefficients(const Array<int> & attr,
@@ -211,8 +211,8 @@ public:
   { pieces.erase(attr); }

   /// Evaluate the coefficient.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// A general function coefficient
@@ -254,8 +254,8 @@ public:
   }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// A common base class for returning individual components of the domain's
@@ -271,8 +271,8 @@ protected:

 public:
   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient which returns the x-component of the evaluation point
@@ -307,8 +307,8 @@ public:
   CylindricalRadialCoefficient() : transip(3) {}

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient which returns the angular position or azimuth (often
@@ -323,8 +323,8 @@ public:
   CylindricalAzimuthalCoefficient() : transip(3) {}

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient which returns the height or altitude of
@@ -342,8 +342,8 @@ public:
   SphericalRadialCoefficient() : transip(3) {}

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient which returns the azimuthal angle (often denoted by phi)
@@ -357,8 +357,8 @@ public:
   SphericalAzimuthalCoefficient() : transip(3) {}

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient which returns the polar angle (often denoted by theta)
@@ -372,8 +372,8 @@ public:
   SphericalPolarCoefficient() : transip(3) {}

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 class GridFunction;
@@ -399,15 +399,15 @@ public:
   const GridFunction * GetGridFunction() const { return GridF; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;

   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
   /// the quadrature points.
   ///
   /// This function uses the efficient QuadratureFunction::ProjectGridFunction
   /// to fill the QuadratureFunction.
-   virtual void Project(QuadratureFunction &qf);
+   void Project(QuadratureFunction &qf) override;
 };


@@ -433,10 +433,10 @@ public:
      : Q1(q1), Q2(q2), Transform2(std::move(F)) { Transform1 = 0; }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;
 };

 /** @brief Delta function coefficient optionally multiplied by a weight
@@ -488,7 +488,7 @@ public:
   }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Set the center location of the delta function.
   void SetDeltaCenter(const Vector& center);
@@ -534,7 +534,7 @@ public:
   virtual real_t EvalDelta(ElementTransformation &T, const IntegrationPoint &ip);
   /** @brief A DeltaFunction cannot be evaluated. Calling this method will
       cause an MFEM error, terminating the application. */
-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
   { mfem_error("DeltaCoefficient::Eval"); return 0.; }
   virtual ~DeltaCoefficient() { delete weight; }
 };
@@ -555,10 +555,10 @@ public:
   { c = &c_; attr.Copy(active_attr); }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override
   { return active_attr[T.Attribute-1] ? c->Eval(T, ip, GetTime()) : 0.0; }
 };

@@ -628,8 +628,8 @@ public:
   using VectorCoefficient::Eval;

   ///  Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip) { V = vec; }
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override { V = vec; }

   /// Return a reference to the constant vector in this class.
   const Vector& GetVec() const { return vec; }
@@ -698,7 +698,7 @@ public:
      : VectorCoefficient(vd) { InitMap(attr, coefs); }

   /// Set the time for time dependent coefficients
-   virtual void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Replace a set of coefficients
   void UpdateCoefficients(const Array<int> & attr,
@@ -713,8 +713,8 @@ public:
   { pieces.erase(attr); }

   /// Evaluate the coefficient.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -728,8 +728,8 @@ public:

   using VectorCoefficient::Eval;
   /// Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   virtual ~PositionVectorCoefficient() { }
 };
@@ -765,8 +765,8 @@ public:

   using VectorCoefficient::Eval;
   /// Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   virtual ~VectorFunctionCoefficient() { }
 };
@@ -787,7 +787,7 @@ public:
   explicit VectorArrayCoefficient(int dim);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Returns i'th coefficient.
   Coefficient* GetCoeff(int i) { return Coeff[i]; }
@@ -806,8 +806,8 @@ public:
   using VectorCoefficient::Eval;
   /** @brief Evaluate the coefficient. Each element of vector V comes from the
       associated array of scalar coefficients. */
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   /// Destroys vector coefficient.
   virtual ~VectorArrayCoefficient();
@@ -836,21 +836,21 @@ public:
   const GridFunction * GetGridFunction() const { return GridFunc; }

   /// Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   /** @brief Evaluate the vector coefficients at all of the locations in the
       integration rule and write the vectors into the columns of matrix @a
       M. */
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationRule &ir);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationRule &ir) override;

   /// @brief Fill the QuadratureFunction @a qf by evaluating the coefficient at
   /// the quadrature points.
   ///
   /// This function uses the efficient QuadratureFunction::ProjectGridFunction
   /// to fill the QuadratureFunction.
-   virtual void Project(QuadratureFunction &qf);
+   void Project(QuadratureFunction &qf) override;

   virtual ~VectorGridFunctionCoefficient() { }
 };
@@ -874,14 +874,14 @@ public:
   const GridFunction * GetGridFunction() const { return GridFunc; }

   /// Evaluate the gradient vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   /** @brief Evaluate the gradient vector coefficient at all of the locations
       in the integration rule and write the vectors into columns of matrix @a
       M. */
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationRule &ir);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationRule &ir) override;

   virtual ~GradientGridFunctionCoefficient() { }
 };
@@ -905,8 +905,8 @@ public:

   using VectorCoefficient::Eval;
   /// Evaluate the vector curl coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   virtual ~CurlGridFunctionCoefficient() { }
 };
@@ -929,8 +929,8 @@ public:
   const GridFunction * GetGridFunction() const { return GridFunc; }

   /// Evaluate the scalar divergence coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;

   virtual ~DivergenceGridFunctionCoefficient() { }
 };
@@ -973,7 +973,7 @@ public:
      : VectorCoefficient(dir_.Size()), dir(dir_), d(x,y,z,s) { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Replace the associated DeltaCoefficient with a new DeltaCoefficient.
   /** The new DeltaCoefficient cannot have a specified weight Coefficient, i.e.
@@ -998,8 +998,8 @@ public:
   using VectorCoefficient::Eval;
   /** @brief A VectorDeltaFunction cannot be evaluated. Calling this method
       will cause an MFEM error, terminating the application. */
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip)
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override
   { mfem_error("VectorDeltaCoefficient::Eval"); }
   virtual ~VectorDeltaCoefficient() { }
 };
@@ -1021,17 +1021,17 @@ public:
   { c = &vc; attr.Copy(active_attr); }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   /** @brief Evaluate the vector coefficient at all of the locations in the
       integration rule and write the vectors into the columns of matrix @a
       M. */
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationRule &ir);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationRule &ir) override;
 };

 typedef VectorCoefficient DiagonalMatrixCoefficient;
@@ -1113,8 +1113,8 @@ public:
      : MatrixCoefficient(m.Height(), m.Width()), mat(m) { }
   using MatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip) { M = mat; }
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override { M = mat; }
   /// Return a reference to the constant matrix.
   const DenseMatrix& GetMatrix() { return mat; }
 };
@@ -1207,7 +1207,7 @@ public:
      : MatrixCoefficient(h, w, symm) { InitMap(attr, coefs); }

   /// Set the time for time dependent coefficients
-   virtual void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Replace a set of coefficients
   void UpdateCoefficients(const Array<int> & attr,
@@ -1222,8 +1222,8 @@ public:
   { pieces.erase(attr); }

   /// Evaluate the coefficient.
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /** @brief A matrix coefficient with an optional scalar coefficient multiplier
@@ -1280,16 +1280,16 @@ public:
   { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   /// (DEPRECATED) Evaluate the symmetric matrix coefficient at @a ip.
   /** @deprecated Use Eval() instead. */
-   virtual void EvalSymmetric(Vector &K, ElementTransformation &T,
-                              const IntegrationPoint &ip);
+   void EvalSymmetric(Vector &K, ElementTransformation &T,
+                      const IntegrationPoint &ip) override;

   virtual ~MatrixFunctionCoefficient() { }
 };
@@ -1310,7 +1310,7 @@ public:
   explicit MatrixArrayCoefficient (int dim);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Get the coefficient located at (i,j) in the matrix.
   Coefficient* GetCoeff (int i, int j) { return Coeff[i*width+j]; }
@@ -1328,8 +1328,8 @@ public:
   { return Coeff[i*width+j] ? Coeff[i*width+j] -> Eval(T, ip, GetTime()) : 0.0; }

   /// Evaluate the matrix coefficient @a ip.
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   virtual ~MatrixArrayCoefficient();
 };
@@ -1392,11 +1392,11 @@ public:
   { c = &mc; attr.Copy(active_attr); }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Coefficients based on sums, products, or other functions of coefficients.
@@ -1425,7 +1425,7 @@ public:
      : aConst(0.0), a(&A), b(&B), alpha(alpha_), beta(beta_) { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first term in the linear combination as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1453,8 +1453,8 @@ public:
   real_t GetBeta() const { return beta; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   {
      return alpha * ((a == NULL ) ? aConst : a->Eval(T, ip) )
             + beta * b->Eval(T, ip);
@@ -1502,8 +1502,8 @@ public:
       @note When this method is called, the caller must make sure that the
       IntegrationPoint associated with @a T is the same as @a ip. This can be
       achieved by calling T.SetIntPoint(&ip). */
-   virtual void Eval(DenseMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;


   /// @deprecated Return a reference to the internal matrix used when evaluating this coefficient as a DenseMatrix.
@@ -1525,8 +1525,8 @@ public:
      : SymmetricMatrixCoefficient(m.Height()), mat(m) { }
   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip) { M = mat; }
+   void Eval(DenseSymmetricMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override { M = mat; }

   /// Return a reference to the constant matrix.
   const DenseSymmetricMatrix& GetMatrix() { return mat; }
@@ -1576,12 +1576,12 @@ public:
   { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   using SymmetricMatrixCoefficient::Eval;
   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseSymmetricMatrix &K, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

   virtual ~SymmetricMatrixFunctionCoefficient() { }
 };
@@ -1606,7 +1606,7 @@ public:
      : aConst(0.0), a(&A), b(&B) { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first term in the product as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1624,8 +1624,8 @@ public:
   Coefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   { return ((a == NULL ) ? aConst : a->Eval(T, ip) ) * b->Eval(T, ip); }
 };

@@ -1654,7 +1654,7 @@ public:
      : aConst(0.0), bConst(B), a(&A), b(NULL) { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the numerator in the ratio as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1677,8 +1677,8 @@ public:
   Coefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   {
      real_t den = (b == NULL ) ? bConst : b->Eval(T, ip);
      MFEM_ASSERT(den != 0.0, "Division by zero in RatioCoefficient");
@@ -1700,7 +1700,7 @@ public:
      : a(&A), p(p_) { }

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the base coefficient
   void SetACoef(Coefficient &A) { a = &A; }
@@ -1713,8 +1713,8 @@ public:
   real_t GetExponent() const { return p; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip)
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override
   { return pow(a->Eval(T, ip), p); }
 };

@@ -1733,7 +1733,7 @@ public:
   InnerProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first vector in the inner product
   void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1746,8 +1746,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient defined as a cross product of two vectors in the xy-plane.
@@ -1765,7 +1765,7 @@ public:
   VectorRotProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first vector in the product
   void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1778,8 +1778,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient defined as the determinant of a matrix coefficient
@@ -1795,7 +1795,7 @@ public:
   DeterminantCoefficient(MatrixCoefficient &A);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -1803,8 +1803,8 @@ public:
   MatrixCoefficient * GetACoef() const { return a; }

   /// Evaluate the determinant coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Scalar coefficient defined as the trace of a matrix coefficient
@@ -1820,7 +1820,7 @@ public:
   TraceCoefficient(MatrixCoefficient &A);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -1828,8 +1828,8 @@ public:
   MatrixCoefficient * GetACoef() const { return a; }

   /// Evaluate the trace coefficient at @a ip.
-   virtual real_t Eval(ElementTransformation &T,
-                       const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T,
+               const IntegrationPoint &ip) override;
 };

 /// Vector coefficient defined as the linear combination of two vectors
@@ -1866,7 +1866,7 @@ public:
                        Coefficient &alpha_, Coefficient &beta_);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first vector coefficient
   void SetACoef(VectorCoefficient &A_) { ACoef = &A_; }
@@ -1909,8 +1909,8 @@ public:
   real_t GetBeta() const { return beta; }

   /// Evaluate the coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -1930,7 +1930,7 @@ public:
   ScalarVectorProductCoefficient(Coefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the scalar factor as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -1948,8 +1948,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -1971,7 +1971,7 @@ public:
   NormalizedVectorCoefficient(VectorCoefficient &A, real_t tol = 1e-6);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the vector coefficient
   void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -1979,8 +1979,8 @@ public:
   VectorCoefficient * GetACoef() const { return a; }

   /// Evaluate the coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -1999,7 +1999,7 @@ public:
   VectorCrossProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first term in the product
   void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -2012,8 +2012,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -2033,7 +2033,7 @@ public:
   MatrixVectorProductCoefficient(MatrixCoefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2046,8 +2046,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the vector coefficient at @a ip.
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
   using VectorCoefficient::Eval;
 };

@@ -2066,8 +2066,8 @@ public:
      : MatrixCoefficient(d, d), dim(d) { }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the linear combination of two matrices
@@ -2088,7 +2088,7 @@ public:
                        real_t alpha_ = 1.0, real_t beta_ = 1.0);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2111,8 +2111,8 @@ public:
   real_t GetBeta() const { return beta; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the product of two matrices
@@ -2140,8 +2140,8 @@ public:
   MatrixCoefficient * GetBCoef() const { return b; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /** @brief Matrix coefficient defined as a product of a scalar coefficient and a
@@ -2161,7 +2161,7 @@ public:
   ScalarMatrixProductCoefficient(Coefficient &A, MatrixCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the scalar factor as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -2179,8 +2179,8 @@ public:
   MatrixCoefficient * GetBCoef() const { return b; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the transpose of a matrix coefficient
@@ -2194,7 +2194,7 @@ public:
   TransposeMatrixCoefficient(MatrixCoefficient &A);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2202,8 +2202,8 @@ public:
   MatrixCoefficient * GetACoef() const { return a; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the inverse of a matrix coefficient.
@@ -2217,7 +2217,7 @@ public:
   InverseMatrixCoefficient(MatrixCoefficient &A);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2225,8 +2225,8 @@ public:
   MatrixCoefficient * GetACoef() const { return a; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the exponential of a matrix coefficient.
@@ -2240,7 +2240,7 @@ public:
   ExponentialMatrixCoefficient(MatrixCoefficient &A);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the matrix coefficient
   void SetACoef(MatrixCoefficient &A) { a = &A; }
@@ -2248,8 +2248,8 @@ public:
   MatrixCoefficient * GetACoef() const { return a; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /// Matrix coefficient defined as the outer product of two vector coefficients.
@@ -2267,7 +2267,7 @@ public:
   OuterProductCoefficient(VectorCoefficient &A, VectorCoefficient &B);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the first vector in the outer product
   void SetACoef(VectorCoefficient &A) { a = &A; }
@@ -2280,8 +2280,8 @@ public:
   VectorCoefficient * GetBCoef() const { return b; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };

 /** @brief Matrix coefficient defined as -a k x k x, for a vector k and scalar a
@@ -2305,7 +2305,7 @@ public:
   CrossCrossCoefficient(Coefficient &A, VectorCoefficient &K);

   /// Set the time for internally stored coefficients
-   void SetTime(real_t t);
+   void SetTime(real_t t) override;

   /// Reset the scalar factor as a constant
   void SetAConst(real_t A) { a = NULL; aConst = A; }
@@ -2323,8 +2323,8 @@ public:
   VectorCoefficient * GetKCoef() const { return k; }

   /// Evaluate the matrix coefficient at @a ip.
-   virtual void Eval(DenseMatrix &M, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(DenseMatrix &M, ElementTransformation &T,
+             const IntegrationPoint &ip) override;
 };
 ///@}

@@ -2349,10 +2349,10 @@ public:
   const QuadratureFunction& GetQuadFunction() const { return QuadF; }

   using VectorCoefficient::Eval;
-   virtual void Eval(Vector &V, ElementTransformation &T,
-                     const IntegrationPoint &ip);
+   void Eval(Vector &V, ElementTransformation &T,
+             const IntegrationPoint &ip) override;

-   virtual void Project(QuadratureFunction &qf);
+   void Project(QuadratureFunction &qf) override;

   virtual ~VectorQuadratureFunctionCoefficient() { }
 };
@@ -2371,9 +2371,9 @@ public:

   const QuadratureFunction& GetQuadFunction() const { return QuadF; }

-   virtual real_t Eval(ElementTransformation &T, const IntegrationPoint &ip);
+   real_t Eval(ElementTransformation &T, const IntegrationPoint &ip) override;

-   virtual void Project(QuadratureFunction &qf);
+   void Project(QuadratureFunction &qf) override;

   virtual ~QuadratureFunctionCoefficient() { }
 };
@@ -943,6 +943,7 @@ void ParaViewDataCollection::Save()
            pvtu_out << "<PDataArray type=\"" << GetDataTypeString()
                     << "\" Name=\"" << field_it.first
                     << "\" NumberOfComponents=\"" << vec_dim << "\" "
+                     << VTKComponentLabels(vec_dim) << " "
                     << "format=\"" << GetDataFormatString() << "\" />\n";
         }
         pvtu_out << "</PPointData>\n";
@@ -977,6 +978,7 @@ void ParaViewDataCollection::Save()
         pvtu_out << "<PDataArray type=\"" << GetDataTypeString()
                  << "\" Name=\"" << q_field_name
                  << "\" NumberOfComponents=\"" << vec_dim << "\" "
+                  << VTKComponentLabels(vec_dim) << " "
                  << "format=\"" << GetDataFormatString() << "\" />\n";
         pvtu_out << "</PPointData>\n";
         WritePVTUFooter(pvtu_out, q_field_name);
@@ -1069,8 +1071,9 @@ void ParaViewDataCollection::SaveGFieldVTU(std::ostream &os, int ref_,
   int vec_dim = it->second->VectorDim();
   os << "<DataArray type=\"" << GetDataTypeString()
      << "\" Name=\"" << it->first
-      << "\" NumberOfComponents=\"" << vec_dim << "\""
-      << " format=\"" << GetDataFormatString() << "\" >" << '\n';
+      << "\" NumberOfComponents=\"" << vec_dim << "\" "
+      << VTKComponentLabels(vec_dim) << " "
+      << "format=\"" << GetDataFormatString() << "\" >" << '\n';
   if (vec_dim == 1)
   {
      // scalar data
@@ -454,28 +454,28 @@ public:
 #endif

   /// Set/change the mesh associated with the collection
-   virtual void SetMesh(Mesh *new_mesh) override;
+   void SetMesh(Mesh *new_mesh) override;

 #ifdef MFEM_USE_MPI
   /// Set/change the mesh associated with the collection.
-   virtual void SetMesh(MPI_Comm comm, Mesh *new_mesh) override;
+   void SetMesh(MPI_Comm comm, Mesh *new_mesh) override;
 #endif

   /// Add a grid function to the collection and update the root file
-   virtual void RegisterField(const std::string& field_name,
-                              GridFunction *gf) override;
+   void RegisterField(const std::string& field_name,
+                      GridFunction *gf) override;

   /// Add a quadrature function to the collection and update the root file.
   /** Visualization of quadrature function is not supported in VisIt(3.12).
       A patch has been sent to VisIt developers in June 2020. */
-   virtual void RegisterQField(const std::string& q_field_name,
-                               QuadratureFunction *qf) override;
+   void RegisterQField(const std::string& q_field_name,
+                       QuadratureFunction *qf) override;

   /// Set the number of digits used for both the cycle and the MPI rank
   /// @note VisIt seems to require 6 pad digits for the MPI rank. Therefore,
   /// this function uses this default value. This behavior can be overridden
   /// by calling SetPadDigitsCycle() and SetPadDigitsRank() instead.
-   virtual void SetPadDigits(int digits) override
+   void SetPadDigits(int digits) override
   { pad_digits_cycle=digits; pad_digits_rank=6; }

   /// Set VisIt parameter: default levels of detail for the MultiresControl
@@ -489,13 +489,13 @@ public:
   void DeleteAll();

   /// Save the collection and a VisIt root file
-   virtual void Save() override;
+   void Save() override;

   /// Save a VisIt root file for the collection
   void SaveRootFile();

   /// Load the collection based on its VisIt data (described in its root file)
-   virtual void Load(int cycle_ = 0) override;
+   void Load(int cycle_ = 0) override;

   /// We will delete the mesh and fields if we own them
   virtual ~VisItDataCollection() {}
@@ -546,7 +546,7 @@ public:

   /// Save the collection - the directory name is constructed based on the
   /// cycle value
-   virtual void Save() override;
+   void Save() override;

   /// Set the data format for the ParaView output files. Possible options are
   /// VTKFormat::ASCII, VTKFormat::BINARY, and VTKFormat::BINARY32.
@@ -590,7 +590,7 @@ public:
   void UseRestartMode(bool restart_mode_);

   /// Load the collection - not implemented in the ParaView writer
-   virtual void Load(int cycle_ = 0) override;
+   void Load(int cycle_ = 0) override;
 };

 }
@@ -52,6 +52,15 @@ protected:
   const DenseMatrix &EvalTransAdjugateJ();
   const DenseMatrix &EvalInverseJ();

+   /// @name Tolerance used for point comparisons
+   ///@{
+#ifdef MFEM_USE_DOUBLE
+   static constexpr real_t tol_0 = 1e-15;
+#elif defined(MFEM_USE_SINGLE)
+   static constexpr real_t tol_0 = 1e-7;
+#endif
+   ///@}
+
 public:

   /** This enumeration declares the values stored in
@@ -176,7 +185,7 @@ public:
       returned. This method is not 100 percent reliable for non-linear
       transformations. */
   virtual int TransformBack(const Vector &pt, IntegrationPoint &ip,
-                             const real_t phys_tol = 1e-15) = 0;
+                             const real_t phys_tol = tol_0) = 0;

   virtual ~ElementTransformation() { }
 };
@@ -281,9 +290,15 @@ public:
        rel_qpts_order(-1),
        solver_type(NewtonElementProject),
        max_iter(16),
+#ifdef MFEM_USE_DOUBLE
        ref_tol(1e-15),
        phys_rtol(1e-15),
        ip_tol(1e-8),
+#elif defined(MFEM_USE_SINGLE)
+        ref_tol(1e-7),
+        phys_rtol(1e-7),
+        ip_tol(1e-4),
+#endif
        print_level(-1)
   { }

@@ -370,10 +385,10 @@ private:

   /** @brief Evaluate the Jacobian of the transformation at the IntPoint and
       store it in dFdx. */
-   virtual const DenseMatrix &EvalJacobian();
+   const DenseMatrix &EvalJacobian() override;
   // Evaluate the Hessian of the transformation at the IntPoint and store it
   // in d2Fdx2.
-   virtual const DenseMatrix &EvalHessian();
+   const DenseMatrix &EvalHessian() override;

 public:
   IsoparametricTransformation() : FElem(NULL) {}
@@ -415,32 +430,32 @@ public:

   /** @brief Transform integration point from reference coordinates to
       physical coordinates and store them in the vector. */
-   virtual void Transform(const IntegrationPoint &, Vector &);
+   void Transform(const IntegrationPoint &, Vector &) override;

   /** @brief Transform all the integration points from the integration rule
       from reference coordinates to physical
      coordinates and store them as column vectors in the matrix. */
-   virtual void Transform(const IntegrationRule &, DenseMatrix &);
+   void Transform(const IntegrationRule &, DenseMatrix &) override;

   /** @brief Transform all the integration points from the column vectors
       of @a matrix from reference coordinates to physical
       coordinates and store them as column vectors in @a result. */
-   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
+   void Transform(const DenseMatrix &matrix, DenseMatrix &result) override;

   /// Return the order of the current element we are using for the transformation.
-   virtual int Order() const { return FElem->GetOrder(); }
+   int Order() const override { return FElem->GetOrder(); }

   /// Return the order of the elements of the Jacobian of the transformation.
-   virtual int OrderJ() const;
+   int OrderJ() const override;

   /** @brief Return the order of the determinant of the Jacobian (weight)
       of the transformation. */
-   virtual int OrderW() const;
+   int OrderW() const override;

   /// Return the order of $ adj(J)^T \nabla fi $
-   virtual int OrderGrad(const FiniteElement *fe) const;
+   int OrderGrad(const FiniteElement *fe) const override;

-   virtual int GetSpaceDim() const { return PointMat.Height(); }
+   int GetSpaceDim() const override { return PointMat.Height(); }

   /** @brief Transform a point @a pt from physical space to a point @a ip in
       reference space and optionally can set a solver tolerance using @a phys_tol. */
@@ -448,8 +463,8 @@ public:
       point in physical space. If the inversion fails a non-zero value is
       returned. This method is not 100 percent reliable for non-linear
       transformations. */
-   virtual int TransformBack(const Vector & v, IntegrationPoint & ip,
-                             const real_t phys_rel_tol = 1e-15)
+   int TransformBack (const Vector & v, IntegrationPoint & ip,
+                      const real_t phys_rel_tol = tol_0) override
   {
      InverseElementTransformation inv_tr(this);
      inv_tr.SetPhysicalRelTol(phys_rel_tol);
@@ -589,9 +604,9 @@ public:
       has been configured. */
   const IntegrationPoint &GetElement2IntPoint() { return eip2; }

-   virtual void Transform(const IntegrationPoint &, Vector &);
-   virtual void Transform(const IntegrationRule &, DenseMatrix &);
-   virtual void Transform(const DenseMatrix &matrix, DenseMatrix &result);
+   void Transform(const IntegrationPoint &, Vector &) override;
+   void Transform(const IntegrationRule &, DenseMatrix &) override;
+   void Transform(const DenseMatrix &matrix, DenseMatrix &result) override;

   ElementTransformation & GetElement1Transformation();
   ElementTransformation & GetElement2Transformation();
@@ -172,10 +172,10 @@ public:
   void SetFluxAveraging(int fa) { flux_averaging = fa; }

   /// Return the total error from the last error estimate.
-   virtual real_t GetTotalError() const override { return total_error; }
+   real_t GetTotalError() const override { return total_error; }

   /// Get a Vector with all element errors.
-   virtual const Vector &GetLocalErrors() override
+   const Vector &GetLocalErrors() override
   {
      if (MeshIsModified()) { ComputeEstimates(); }
      return error_estimates;
@@ -184,14 +184,14 @@ public:
   /** @brief Get an Array<int> with anisotropic flags for all mesh elements.
       Return an empty array when anisotropic estimates are not available or
       enabled. */
-   virtual const Array<int> &GetAnisotropicFlags() override
+   const Array<int> &GetAnisotropicFlags() override
   {
      if (MeshIsModified()) { ComputeEstimates(); }
      return aniso_flags;
   }

   /// Reset the error estimator.
-   virtual void Reset() override { current_sequence = -1; }
+   void Reset() override { current_sequence = -1; }

   /** @brief Destroy a ZienkiewiczZhuEstimator object. Destroys, if owned, the
       FiniteElementSpace, flux_space. */
@@ -298,17 +298,17 @@ public:
   }

   /// Return the total error from the last error estimate.
-   virtual real_t GetTotalError() const override { return total_error; }
+   real_t GetTotalError() const override { return total_error; }

   /// Get a Vector with all element errors.
-   virtual const Vector &GetLocalErrors() override
+   const Vector &GetLocalErrors() override
   {
      if (MeshIsModified()) { ComputeEstimates(); }
      return error_estimates;
   }

   /// Reset the error estimator.
-   virtual void Reset() override { current_sequence = -1; }
+   void Reset() override { current_sequence = -1; }

   virtual ~LSZienkiewiczZhuEstimator() { }
 };
@@ -411,17 +411,17 @@ public:
   void SetLocalErrorNormP(int p) { local_norm_p = p; }

   /// Return the total error from the last error estimate.
-   virtual real_t GetTotalError() const override { return total_error; }
+   real_t GetTotalError() const override { return total_error; }

   /// Get a Vector with all element errors.
-   virtual const Vector &GetLocalErrors() override
+   const Vector &GetLocalErrors() override
   {
      if (MeshIsModified()) { ComputeEstimates(); }
      return error_estimates;
   }

   /// Reset the error estimator.
-   virtual void Reset() override { current_sequence = -1; }
+   void Reset() override { current_sequence = -1; }

   /** @brief Destroy a L2ZienkiewiczZhuEstimator object. Destroys, if owned,
       the FiniteElementSpace, flux_space. */
@@ -505,10 +505,10 @@ public:
   void SetCoef(VectorCoefficient &A) { vcoef = &A; }

   /// Reset the error estimator.
-   virtual void Reset() override { current_sequence = -1; }
+   void Reset() override { current_sequence = -1; }

   /// Get a Vector with all element errors.
-   virtual const Vector &GetLocalErrors() override
+   const Vector &GetLocalErrors() override
   {
      if (MeshIsModified()) { ComputeEstimates(); }
      return error_estimates;
@@ -661,7 +661,7 @@ public:
   /// Reset the error estimator.
   void Reset() override { current_sequence = -1; };

-   virtual real_t GetTotalError() const override { return total_error; }
+   real_t GetTotalError() const override { return total_error; }

   /** @brief Change the method to compute hₑ on a per-element basis.
       @param compute_element_coefficient_
@@ -394,7 +394,32 @@ public:
   /// Get a const reference to the nodes of the element
   const IntegrationRule & GetNodes() const { return Nodes; }

-   // virtual functions for finite elements on vector spaces
+   /** @brief Evaluate the Hessians of all shape functions of a scalar finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
+       part of the Hessian of one shape function.
+       The order in 2D is {u_xx, u_xy, u_yy}.
+       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
+   virtual void CalcHessian(const IntegrationPoint &ip,
+                            DenseMatrix &Hessian) const;
+
+   /** @brief Evaluate the Hessian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof, #dim*(#dim+1)/2) of @a Hessian must be set in advance. */
+   void CalcPhysHessian(ElementTransformation &Trans,
+                        DenseMatrix& Hessian) const;
+
+   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof) of @a Laplacian must be set in advance. */
+   void CalcPhysLaplacian(ElementTransformation &Trans,
+                          Vector& Laplacian) const;
+
+   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
+       element in physical space at the given point @a ip. */
+   /** The size (#dof) of @a Laplacian must be set in advance. */
+   void CalcPhysLinLaplacian(ElementTransformation &Trans,
+                             Vector& Laplacian) const;

   /** @brief Evaluate the values of all shape functions of a *vector* finite
       element in reference space at the given point @a ip. */
@@ -454,30 +479,6 @@ public:
   */
   virtual void GetFaceDofs(int face, int **dofs, int *ndofs) const;

-   /** @brief Evaluate the Hessians of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** Each row of the result DenseMatrix @a Hessian contains upper triangular
-       part of the Hessian of one shape function.
-       The order in 2D is {u_xx, u_xy, u_yy}.
-       The size (#dof x (#dim (#dim+1)/2) of @a Hessian must be set in advance.*/
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
-
-   /** @brief Evaluate the Hessian of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** The size (#dof, #dim*(#dim+1)/2) of @a Hessian must be set in advance. */
-   virtual void CalcPhysHessian(ElementTransformation &Trans,
-                                DenseMatrix& Hessian) const;
-
-   /** @brief Evaluate the Laplacian of all shape functions of a scalar finite
-       element in reference space at the given point @a ip. */
-   /** The size (#dof) of @a Laplacian must be set in advance. */
-   virtual void CalcPhysLaplacian(ElementTransformation &Trans,
-                                  Vector& Laplacian) const;
-
-   virtual void CalcPhysLinLaplacian(ElementTransformation &Trans,
-                                     Vector& Laplacian) const;
-
   /** @brief Return the local interpolation matrix @a I (Dof x Dof) where the
       fine element is the image of the base geometry under the given
       transformation. */
@@ -28,12 +28,12 @@ private:
 public:
   /// Construct the H1_SegmentElement of order @a p and BasisType @a btype
   H1_SegmentElement(const int p, const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &Hessian) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -49,12 +49,12 @@ public:
   /// Construct the H1_QuadrilateralElement of order @a p and BasisType @a btype
   H1_QuadrilateralElement(const int p,
                           const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &Hessian) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -70,12 +70,12 @@ private:
 public:
   /// Construct the H1_HexahedronElement of order @a p and BasisType @a btype
   H1_HexahedronElement(const int p, const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &Hessian) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &Hessian) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -93,11 +93,11 @@ private:
 public:
   /// Construct the H1_TriangleElement of order @a p and BasisType @a btype
   H1_TriangleElement(const int p, const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &ddshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &ddshape) const override;
 };


@@ -117,11 +117,11 @@ public:
   /// Construct the H1_TetrahedronElement of order @a p and BasisType @a btype
   H1_TetrahedronElement(const int p,
                         const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian(const IntegrationPoint &ip,
-                            DenseMatrix &ddshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian(const IntegrationPoint &ip,
+                    DenseMatrix &ddshape) const override;
 };


@@ -143,9 +143,9 @@ public:
   /// Construct the H1_WedgeElement of order @a p and BasisType @a btype
   H1_WedgeElement(const int p,
                   const int btype = BasisType::GaussLobatto);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };

 } // namespace mfem
@@ -28,13 +28,13 @@ private:
 public:
   /// Construct the L2_SegmentElement of order @a p and BasisType @a btype
   L2_SegmentElement(const int p, const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

 };
@@ -52,25 +52,25 @@ public:
   /// Construct the L2_QuadrilateralElement of order @a p and BasisType @a btype
   L2_QuadrilateralElement(const int p,
                           const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_2D(fe, Trans, curl); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

   using FiniteElement::Project;
-   virtual void ProjectDiv(const FiniteElement &fe,
-                           ElementTransformation &Trans,
-                           DenseMatrix &div) const;
-   virtual void Project(Coefficient &coeff,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void ProjectDiv(const FiniteElement &fe,
+                   ElementTransformation &Trans,
+                   DenseMatrix &div) const override;
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };


@@ -86,21 +86,21 @@ public:
   /// Construct the L2_HexahedronElement of order @a p and BasisType @a btype
   L2_HexahedronElement(const int p,
                        const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

   using FiniteElement::Project;
-   virtual void ProjectDiv(const FiniteElement &fe,
-                           ElementTransformation &Trans,
-                           DenseMatrix &div) const;
-   virtual void Project(Coefficient &coeff,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void ProjectDiv(const FiniteElement &fe,
+                   ElementTransformation &Trans,
+                   DenseMatrix &div) const override;
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };


@@ -118,17 +118,17 @@ public:
   /// Construct the L2_TriangleElement of order @a p and BasisType @a btype
   L2_TriangleElement(const int p,
                      const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_2D(fe, Trans, curl); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

 };
@@ -149,13 +149,13 @@ public:
   /// Construct the L2_TetrahedronElement of order @a p and BasisType @a btype
   L2_TetrahedronElement(const int p,
                         const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

 };
@@ -178,9 +178,9 @@ public:
   /// Construct the L2_WedgeElement of order @a p and BasisType @a btype
   L2_WedgeElement(const int p,
                   const int btype = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };

 } // namespace mfem
@@ -36,62 +36,63 @@ public:
                        const int cb_type = BasisType::GaussLobatto,
                        const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }

-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   {
      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
      else { Project_ND(tk, dof2tk, vc, Trans, dofs); }
   }

-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }

-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }

-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }

-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }

-   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+   void GetFaceMap(const int face_id, Array<int> &face_map) const override;

 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
@@ -118,46 +119,47 @@ public:
   ND_QuadrilateralElement(const int p,
                           const int cb_type = BasisType::GaussLobatto,
                           const int ob_type = BasisType::GaussLegendre);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }
-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   {
      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
      else { Project_ND(tk, dof2tk, vc, Trans, dofs); }
   }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

-   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+   void GetFaceMap(const int face_id, Array<int> &face_map) const override;

 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
@@ -184,47 +186,48 @@ class ND_TetrahedronElement : public VectorFiniteElement
 public:
   /// Construct the ND_TetrahedronElement of order @a p
   ND_TetrahedronElement(const int p);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }
-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
-   virtual const StatelessDofTransformation *GetDofTransformation() const
+   const StatelessDofTransformation *GetDofTransformation() const override
   { return &doftrans; }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
 };

@@ -247,42 +250,43 @@ class ND_TriangleElement : public VectorFiniteElement
 public:
   /// Construct the ND_TriangleElement of order @a p
   ND_TriangleElement(const int p);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }
-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
-   virtual const StatelessDofTransformation *GetDofTransformation() const
+   const StatelessDofTransformation *GetDofTransformation() const override
   { return &doftrans; }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
 };

@@ -298,39 +302,40 @@ public:
   /** @brief Construct the ND_SegmentElement of order @a p and open
       BasisType @a ob_type */
   ND_SegmentElement(const int p, const int ob_type = BasisType::GaussLegendre);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override
   { obasis1d.Eval(ip.x, shape); }
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }
-   // virtual void CalcCurlShape(const IntegrationPoint &ip,
+   // void CalcCurlShape(const IntegrationPoint &ip,
   //                            DenseMatrix &curl_shape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }
 };

@@ -358,53 +363,54 @@ public:
                   const int cb_type = BasisType::GaussLobatto,
                   const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_ND(Trans, shape); }

-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }

-   virtual const StatelessDofTransformation *GetDofTransformation() const
+   const StatelessDofTransformation *GetDofTransformation() const override
   { return &doftrans; }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }

-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }

-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_ND(tk, dof2tk, fe, Trans, I); }

-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
 };

@@ -423,11 +429,11 @@ public:

   using FiniteElement::CalcVShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;
 };

 /// Arbitrary order, three component, Nedelec elements in 1D on a segment
@@ -455,56 +461,57 @@ public:
   using FiniteElement::CalcVShape;
   using FiniteElement::CalcPhysCurlShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;

-   virtual void CalcPhysCurlShape(ElementTransformation &Trans,
-                                  DenseMatrix &curl_shape) const;
+   void CalcPhysCurlShape(ElementTransformation &Trans,
+                          DenseMatrix &curl_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_ND(*this, tk, dof2tk, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_ND(tk, dof2tk, Trans, R); }

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_ND(CheckVectorFE(fe), tk, dof2tk, Trans, I); }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_ND(tk, dof2tk, vc, Trans, dofs); }

-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_ND(tk, dof2tk, mc, T, dofs); }

-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override;

-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_ND(tk, dof2tk, fe, Trans, grad); }

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_ND(tk, dof2tk, fe, Trans, curl); }
 };

@@ -535,32 +542,32 @@ public:
                         const int cb_type = BasisType::GaussLobatto,
                         const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation(*this, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { MFEM_ABORT("method is not overloaded"); }

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;
 };

 class ND_R2D_FiniteElement : public VectorFiniteElement
@@ -580,35 +587,35 @@ public:
   using FiniteElement::CalcVShape;
   using FiniteElement::CalcPhysCurlShape;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void CalcPhysCurlShape(ElementTransformation &Trans,
-                                  DenseMatrix &curl_shape) const;
+   void CalcPhysCurlShape(ElementTransformation &Trans,
+                          DenseMatrix &curl_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation(*this, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const;
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override;

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override;

-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const;
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override;
 };

 /// Arbitrary order Nedelec 3D elements in 2D on a triangle
@@ -635,10 +642,10 @@ public:
   using ND_R2D_FiniteElement::CalcVShape;
   using ND_R2D_FiniteElement::CalcPhysCurlShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
 };


@@ -664,10 +671,10 @@ public:
   using ND_R2D_FiniteElement::CalcVShape;
   using ND_R2D_FiniteElement::CalcPhysCurlShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcCurlShape(const IntegrationPoint &ip,
-                              DenseMatrix &curl_shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
 };


@@ -398,8 +398,621 @@ void NURBS3DFiniteElement::CalcHessian (const IntegrationPoint &ip,
      hessian(o,5) = hessian(o,5)*sum
                     - 2*du(o,1)*sum*dsum[1]
                     + u[o]*sum*(2*dsum[1]*dsum[1] - d2sum[5]);
-
   }
 }

+
+void NURBS_HDiv2DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+
+   order = max(orders[0]+1, orders[1]+1);
+   dof = (orders[0] + 2)*(orders[1] + 1)
+         + (orders[1] + 1)*(orders[1] + 2);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HDiv2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                           DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         shape(o,0) = shape1_x(i)*sy;
+         shape(o,1) = 0.0;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t sy1 = shape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         shape(o,0) = 0.0;
+         shape(o,1) = shape_x(i)*sy1;
+      }
+   }
+}
+
+void NURBS_HDiv2DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                           DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & J = Trans.Jacobian();
+   MFEM_ASSERT(J.Width() == 2 && J.Height() == 2,
+               "NURBS_HDiv2DFiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      shape(i, 0) = sx * J(0, 0) + sy * J(0, 1);
+      shape(i, 1) = sx * J(1, 0) + sy * J(1, 1);
+   }
+   shape *= (1.0 / Trans.Weight());
+}
+
+void NURBS_HDiv2DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
+                                             Vector &divshape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         divshape(o) = dshape1_x(i)*sy;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t dsy1 = dshape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         divshape(o) = shape_x(i)*dsy1;
+      }
+   }
+}
+
+NURBS_HDiv2DFiniteElement::~NURBS_HDiv2DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+}
+
+
+void NURBS_HDiv3DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+   orders[2] = kv[2]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+   kv1[2] = kv[2]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+   shape_z.SetSize(orders[2]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+   dshape_z.SetSize(orders[2]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+   d2shape_z.SetSize(orders[2]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+   shape1_z.SetSize(orders[2]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+   dshape1_z.SetSize(orders[2]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+   d2shape1_z.SetSize(orders[2]+2);
+
+   order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
+   dof = (orders[0] + 2)*(orders[1] + 1)*(orders[2] + 1) +
+         (orders[0] + 1)*(orders[1] + 2)*(orders[2] + 1) +
+         (orders[0] + 1)*(orders[1] + 1)*(orders[2] + 2);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HDiv3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                           DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape(shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   shape = 0.0;
+   int o = 0;
+   for (int k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz = shape_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,0) = shape1_x(i)*sy_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,1) = shape_x(i)*sy1_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,2) = shape_x(i)*sy_sz1;
+         }
+      }
+   }
+}
+
+void NURBS_HDiv3DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                           DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & J = Trans.Jacobian();
+   MFEM_ASSERT(J.Width() == 3 && J.Height() == 3,
+               "RT_R2D_FiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      real_t sz = shape(i, 2);
+      shape(i, 0) = sx * J(0, 0) + sy * J(0, 1) + sz * J(0, 2);
+      shape(i, 1) = sx * J(1, 0) + sy * J(1, 1) + sz * J(1, 2);
+      shape(i, 2) = sx * J(2, 0) + sy * J(2, 1) + sz * J(2, 2);
+   }
+   shape *= (1.0 / Trans.Weight());
+}
+
+void NURBS_HDiv3DFiniteElement::CalcDivShape(const IntegrationPoint &ip,
+                                             Vector &divshape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+   kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
+
+   int o = 0;
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz = shape_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            divshape(o) = dshape1_x(i)*sy_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t dy1_sz = dshape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            divshape(o) = shape_x(i)*dy1_sz;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t dz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_dz1 = shape_y(j)*dz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            divshape(o) = shape_x(i)*sy_dz1;
+         }
+      }
+   }
+}
+
+NURBS_HDiv3DFiniteElement::~NURBS_HDiv3DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+}
+
+void NURBS_HCurl2DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+
+   order = max(orders[0]+1, orders[1]+1);
+   dof = (orders[0] + 1)*(orders[1] + 2)
+         + (orders[1] + 2)*(orders[1] + 1);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HCurl2DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                            DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t sy1 = shape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         shape(o,0) = shape_x(i)*sy1;
+         shape(o,1) = 0.0;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         shape(o,0) = 0.0;
+         shape(o,1) = shape1_x(i)*sy;
+      }
+   }
+}
+
+void NURBS_HCurl2DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                            DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & JI = Trans.InverseJacobian();
+   MFEM_ASSERT(JI.Width() == 2 && JI.Height() == 2,
+               "NURBS_HCurl2DFiniteElement cannot be embedded in "
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0);
+      shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1);
+   }
+}
+
+void NURBS_HCurl2DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
+                                               DenseMatrix &curl_shape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+
+   int o = 0;
+   for (int j = 0; j <= orders[1]+1; j++)
+   {
+      const real_t dsy1 = dshape1_y(j);
+      for (int i = 0; i <= orders[0]; i++, o++)
+      {
+         curl_shape(o,0) = -shape_x(i)*dsy1;
+      }
+   }
+
+   for (int j = 0; j <= orders[1]; j++)
+   {
+      const real_t sy = shape_y(j);
+      for (int i = 0; i <= orders[0]+1; i++, o++)
+      {
+         curl_shape(o,0) = dshape1_x(i)*sy;
+      }
+   }
+}
+
+NURBS_HCurl2DFiniteElement::~NURBS_HCurl2DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+}
+
+
+void NURBS_HCurl3DFiniteElement::SetOrder() const
+{
+   orders[0] = kv[0]->GetOrder();
+   orders[1] = kv[1]->GetOrder();
+   orders[2] = kv[2]->GetOrder();
+
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+
+   kv1[0] = kv[0]->DegreeElevate(1);
+   kv1[1] = kv[1]->DegreeElevate(1);
+   kv1[2] = kv[2]->DegreeElevate(1);
+
+   shape_x.SetSize(orders[0]+1);
+   shape_y.SetSize(orders[1]+1);
+   shape_z.SetSize(orders[2]+1);
+
+   dshape_x.SetSize(orders[0]+1);
+   dshape_y.SetSize(orders[1]+1);
+   dshape_z.SetSize(orders[2]+1);
+
+   d2shape_x.SetSize(orders[0]+1);
+   d2shape_y.SetSize(orders[1]+1);
+   d2shape_z.SetSize(orders[2]+1);
+
+   shape1_x.SetSize(orders[0]+2);
+   shape1_y.SetSize(orders[1]+2);
+   shape1_z.SetSize(orders[2]+2);
+
+   dshape1_x.SetSize(orders[0]+2);
+   dshape1_y.SetSize(orders[1]+2);
+   dshape1_z.SetSize(orders[2]+2);
+
+   d2shape1_x.SetSize(orders[0]+2);
+   d2shape1_y.SetSize(orders[1]+2);
+   d2shape1_z.SetSize(orders[2]+2);
+
+   order = max(orders[0]+1, max( orders[1]+1, orders[2]+1));
+   dof = (orders[0] + 1)*(orders[1] + 2)*(orders[2] + 2) +
+         (orders[0] + 2)*(orders[1] + 1)*(orders[2] + 2) +
+         (orders[0] + 2)*(orders[1] + 2)*(orders[2] + 1);
+   u.SetSize(dof);
+   du.SetSize(dof);
+   weights.SetSize(dof);
+}
+
+void NURBS_HCurl3DFiniteElement::CalcVShape(const IntegrationPoint &ip,
+                                            DenseMatrix &shape) const
+{
+   kv[0]->CalcShape(shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape(shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape(shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   shape = 0.0;
+   int o = 0;
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz1 = shape1_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            shape(o,0) = shape_x(i)*sy1_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,1) = shape1_x(i)*sy_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            shape(o,2) = shape1_x(i)*sy1_sz;
+         }
+      }
+   }
+}
+
+void NURBS_HCurl3DFiniteElement::CalcVShape(ElementTransformation &Trans,
+                                            DenseMatrix &shape) const
+{
+   CalcVShape(Trans.GetIntPoint(), shape);
+   const DenseMatrix & JI = Trans.InverseJacobian();
+   MFEM_ASSERT(JI.Width() == 3 && JI.Height() == 3,
+               "NURBS_HCurl3DFiniteElement must be in a"
+               "3 dimensional spaces");
+   for (int i=0; i<dof; i++)
+   {
+      real_t sx = shape(i, 0);
+      real_t sy = shape(i, 1);
+      real_t sz = shape(i, 2);
+      shape(i, 0) = sx * JI(0, 0) + sy * JI(1, 0) + sz * JI(2, 0);
+      shape(i, 1) = sx * JI(0, 1) + sy * JI(1, 1) + sz * JI(2, 1);
+      shape(i, 2) = sx * JI(0, 2) + sy * JI(1, 2) + sz * JI(2, 2);
+   }
+}
+
+void NURBS_HCurl3DFiniteElement::CalcCurlShape(const IntegrationPoint &ip,
+                                               DenseMatrix &curl_shape) const
+{
+   kv[0]->CalcShape ( shape_x, ijk[0], ip.x);
+   kv[1]->CalcShape ( shape_y, ijk[1], ip.y);
+   kv[2]->CalcShape ( shape_z, ijk[2], ip.z);
+
+   kv1[0]->CalcShape(shape1_x, ijk[0], ip.x);
+   kv1[1]->CalcShape(shape1_y, ijk[1], ip.y);
+   kv1[2]->CalcShape(shape1_z, ijk[2], ip.z);
+
+   kv1[0]->CalcDShape(dshape1_x, ijk[0], ip.x);
+   kv1[1]->CalcDShape(dshape1_y, ijk[1], ip.y);
+   kv1[2]->CalcDShape(dshape1_z, ijk[2], ip.z);
+
+   int o = 0;
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_dsz1 = shape1_y(j)*dsz1,
+                      dsy1_sz1 = dshape1_y(j)*sz1;
+         for (int i = 0; i <= orders[0]; i++, o++)
+         {
+            curl_shape(o,0) = 0.0;
+            curl_shape(o,1) =  shape_x(i)*sy1_dsz1;
+            curl_shape(o,2) = -shape_x(i)*dsy1_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]+1; k++)
+   {
+      const real_t sz1 = shape1_z(k), dsz1 = dshape1_z(k);
+      for (int j = 0; j <= orders[1]; j++)
+      {
+         const real_t sy_dsz1 = shape_y(j)*dsz1,
+                      sy_sz1 = shape_y(j)*sz1;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            curl_shape(o,0) = -shape1_x(i)*sy_dsz1;
+            curl_shape(o,1) = 0.0;
+            curl_shape(o,2) = dshape1_x(i)*sy_sz1;
+         }
+      }
+   }
+
+   for (int  k = 0; k <= orders[2]; k++)
+   {
+      const real_t sz = shape_z(k);
+      for (int j = 0; j <= orders[1]+1; j++)
+      {
+         const real_t sy1_sz = shape1_y(j)*sz,
+                      dsy1_sz = dshape1_y(j)*sz;
+         for (int i = 0; i <= orders[0]+1; i++, o++)
+         {
+            curl_shape(o,0) = shape1_x(i)*dsy1_sz;
+            curl_shape(o,1) = -dshape1_x(i)*sy1_sz;
+            curl_shape(o,2) = 0.0;
+         }
+      }
+   }
+}
+
+NURBS_HCurl3DFiniteElement::~NURBS_HCurl3DFiniteElement()
+{
+   if (kv1[0]) { delete kv1[0]; }
+   if (kv1[1]) { delete kv1[1]; }
+   if (kv1[2]) { delete kv1[2]; }
+}
+
 }
@@ -20,7 +20,7 @@ namespace mfem
 class KnotVector;

 /// An arbitrary order and dimension NURBS element
-class NURBSFiniteElement : public ScalarFiniteElement
+class NURBSFiniteElement
 {
 protected:
   mutable Array <const KnotVector*> kv;
@@ -30,31 +30,34 @@ protected:

 public:
   /** @brief Construct NURBSFiniteElement with given
-       @param D    Reference space dimension
-       @param G    Geometry type (of type Geometry::Type)
-       @param Do   Number of degrees of freedom in the FiniteElement
-       @param O    Order/degree of the FiniteElement
-       @param F    FunctionSpace type of the FiniteElement
+       @param dim    Reference space dimension
    */
-   NURBSFiniteElement(int D, Geometry::Type G, int Do, int O, int F)
-      : ScalarFiniteElement(D, G, Do, O, F)
+   NURBSFiniteElement(int dim)
   {
      ijk = NULL;
      patch = elem = -1;
      kv.SetSize(dim);
-      weights.SetSize(dof);
-      weights = 1.0;
   }

+   /// Resets the patch and element data stored in the element
   void                 Reset      ()         const { patch = elem = -1; }
+   /// Set which IJK in patch should be evaluated
   void                 SetIJK     (const int *IJK) const { ijk = IJK; }
+   /// Get which patch is currently considered
   int                  GetPatch   ()         const { return patch; }
+   /// Set which patch should be evaluated
   void                 SetPatch   (int p)    const { patch = p; }
+   /// Set which elemenet should be evaluated
   int                  GetElement ()         const { return elem; }
+   /// Get which element is currently considered
   void                 SetElement (int e)    const { elem = e; }
+   /// Get the KnotVectors
   Array <const KnotVector*> &KnotVectors()   const { return kv; }
+   /// Get the Weights
   Vector              &Weights    ()         const { return weights; }
-   /// Update the NURBSFiniteElement according to the currently set knot vectors
+   /// Update the polynomial order according to the currently set knotvectors
+   /// Resizes all internal data members to have the correct size
+   /// related to the polynomial order
   virtual void         SetOrder   ()         const { }

   /// Returns the indices (i,j) in 2D or (i,j,k) in 3D of this element in the
@@ -64,7 +67,8 @@ public:


 /// An arbitrary order 1D NURBS element on a segment
-class NURBS1DFiniteElement : public NURBSFiniteElement
+class NURBS1DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
   mutable Vector shape_x;
@@ -72,19 +76,21 @@ protected:
 public:
   /// Construct the NURBS1DFiniteElement of order @a p
   NURBS1DFiniteElement(int p)
-      : NURBSFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
+      : ScalarFiniteElement(1, Geometry::SEGMENT, p + 1, p, FunctionSpace::Qk),
+        NURBSFiniteElement(1),
        shape_x(p + 1) { }

-   virtual void SetOrder() const;
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian (const IntegrationPoint &ip,
-                             DenseMatrix &hessian) const;
+   void SetOrder() const override;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian (const IntegrationPoint &ip,
+                     DenseMatrix &hessian) const override;
 };

 /// An arbitrary order 2D NURBS element on a square
-class NURBS2DFiniteElement : public NURBSFiniteElement
+class NURBS2DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
   mutable Vector u, shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
@@ -93,30 +99,33 @@ protected:
 public:
   /// Construct the NURBS2DFiniteElement of order @a p
   NURBS2DFiniteElement(int p)
-      : NURBSFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
-                           FunctionSpace::Qk),
+      : ScalarFiniteElement(2, Geometry::SQUARE, (p + 1)*(p + 1), p,
+                            FunctionSpace::Qk),
+        NURBSFiniteElement(2),
        u(dof), shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
        dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1), du(dof,2)
   { orders[0] = orders[1] = p; }

   /// Construct the NURBS2DFiniteElement with x-order @a px and y-order @a py
   NURBS2DFiniteElement(int px, int py)
-      : NURBSFiniteElement(2, Geometry::SQUARE, (px + 1)*(py + 1),
-                           std::max(px, py), FunctionSpace::Qk),
+      : ScalarFiniteElement(2, Geometry::SQUARE, (px + 1)*(py + 1),
+                            std::max(px, py), FunctionSpace::Qk),
+        NURBSFiniteElement(2),
        u(dof), shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
        dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1), du(dof,2)
   { orders[0] = px; orders[1] = py; }

-   virtual void SetOrder() const;
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian (const IntegrationPoint &ip,
-                             DenseMatrix &hessian) const;
+   void SetOrder() const override;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian (const IntegrationPoint &ip,
+                     DenseMatrix &hessian) const override;
 };

 /// An arbitrary order 3D NURBS element on a cube
-class NURBS3DFiniteElement : public NURBSFiniteElement
+class NURBS3DFiniteElement : public ScalarFiniteElement,
+   public NURBSFiniteElement
 {
 protected:
   mutable Vector u, shape_x, shape_y, shape_z;
@@ -127,8 +136,9 @@ protected:
 public:
   /// Construct the NURBS3DFiniteElement of order @a p
   NURBS3DFiniteElement(int p)
-      : NURBSFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
-                           FunctionSpace::Qk),
+      : ScalarFiniteElement(3, Geometry::CUBE, (p + 1)*(p + 1)*(p + 1), p,
+                            FunctionSpace::Qk),
+        NURBSFiniteElement(3),
        u(dof), shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
        dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
        d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1), du(dof,3)
@@ -137,19 +147,366 @@ public:
   /// Construct the NURBS3DFiniteElement with x-order @a px and y-order @a py
   /// and z-order @a pz
   NURBS3DFiniteElement(int px, int py, int pz)
-      : NURBSFiniteElement(3, Geometry::CUBE, (px + 1)*(py + 1)*(pz + 1),
-                           std::max(std::max(px,py),pz), FunctionSpace::Qk),
+      : ScalarFiniteElement(3, Geometry::CUBE, (px + 1)*(py + 1)*(pz + 1),
+                            std::max(std::max(px,py),pz), FunctionSpace::Qk),
+        NURBSFiniteElement(2),
        u(dof), shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
        dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
        d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1), du(dof,3)
   { orders[0] = px; orders[1] = py; orders[2] = pz; }

-   virtual void SetOrder() const;
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void CalcHessian (const IntegrationPoint &ip,
-                             DenseMatrix &hessian) const;
+   void SetOrder() const override;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void CalcHessian (const IntegrationPoint &ip,
+                     DenseMatrix &hessian) const override;
+};
+
+
+/** An arbitrary order H(div)-conforming 2D NURBS element on a square.
+    More details in the following papers:
+
+[1] Annalisa Buffa, Carlo De Falco, Giancarlo Sangalli
+"Isogeometric analysis: stable elements for the 2D Stokes equation."
+International Journal for Numerical Methods in Fluids 65 (11‐12) 1407-1422
+
+[2] John A Evans, Thomas JR Hughes
+"Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations."
+Journal of Computational Physics (241) 141-167
+*/
+class NURBS_HDiv2DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
+   mutable Vector shape1_x, shape1_y, dshape1_x, dshape1_y, d2shape1_x, d2shape1_y;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HDiv2DFiniteElement of order @a p
+   NURBS_HDiv2DFiniteElement(int p)
+      : VectorFiniteElement(2, Geometry::SQUARE, 2*(p + 1)*(p + 2), p,
+                            H_DIV,FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
+        dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), dshape1_x(p + 2),
+        dshape1_y(p + 2), d2shape1_x(p + 2), d2shape1_y(p + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = orders[1] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   /// Construct the NURBS_HDiv2DFiniteElement with x-order @a px and y-order @a py
+   NURBS_HDiv2DFiniteElement(int px, int py)
+      : VectorFiniteElement(2, Geometry::SQUARE,
+                            (px + 2)*(py + 1)+(px + 1)*(py + 2),
+                            std::max(px, py), H_DIV, FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
+        dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1),
+        shape1_x(px + 2), shape1_y(py + 2), dshape1_x(px + 2),
+        dshape1_y(py + 2), d2shape1_x(px + 2), d2shape1_y(py + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = px; orders[1] = py;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   void SetOrder() const override;
+
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the divergence of all shape functions of a *vector*
+       finite element in reference space at the given point @a ip. */
+   /** The size (#dof) of the result Vector @a divshape must be set in advance.
+    */
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+
+   ~NURBS_HDiv2DFiniteElement();
+};
+
+
+/** An arbitrary order H(div)-conforming 3D NURBS element on a cube
+    More details in the following papers:
+
+    [1] Annalisa Buffa, Carlo De Falco, Giancarlo Sangalli
+    "Isogeometric analysis: stable elements for the 2D Stokes equation."
+    International Journal for Numerical Methods in Fluids 65 (11‐12) 1407-1422
+
+    [2] John A Evans, Thomas JR Hughes
+    "Isogeometric divergence-conforming B-splines for the unsteady
+    Navier–Stokes equations."
+    Journal of Computational Physics (241) 141-167 */
+class NURBS_HDiv3DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, shape_z;
+   mutable Vector dshape_x, dshape_y, dshape_z;
+   mutable Vector d2shape_x, d2shape_y, d2shape_z;
+   mutable Vector shape1_x, shape1_y, shape1_z;
+   mutable Vector dshape1_x, dshape1_y, dshape1_z;
+   mutable Vector d2shape1_x, d2shape1_y, d2shape1_z;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HDiv3DFiniteElement of order @a p
+   NURBS_HDiv3DFiniteElement(int p)
+      : VectorFiniteElement(3, Geometry::CUBE, 3*(p + 1)*(p + 1)*(p + 2),
+                            p, H_DIV,FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
+        dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
+        d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), shape1_z(p + 2),
+        dshape1_x(p + 2), dshape1_y(p + 2),dshape1_z(p + 2),
+        d2shape1_x(p + 2), d2shape1_y(p + 2), d2shape1_z(p + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = orders[1] = orders[2] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   /// Construct the NURBS_HDiv3DFiniteElement with x-order @a px, y-order @a py and z-order @a pz
+   NURBS_HDiv3DFiniteElement(int px, int py, int pz)
+      : VectorFiniteElement(3, Geometry::CUBE,
+                            (px + 2)*(py + 1)*(pz + 1) +
+                            (px + 1)*(py + 2)*(pz + 1) +
+                            (px + 1)*(py + 1)*(pz + 2),
+                            std::max(px, py), H_DIV, FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
+        dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
+        d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1),
+        shape1_x(px + 2), shape1_y(py + 2), shape1_z(pz + 2),
+        dshape1_x(px + 2), dshape1_y(py + 2),dshape1_z(pz + 2),
+        d2shape1_x(px + 2), d2shape1_y(py + 2), d2shape1_z(pz + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = px; orders[1] = py; orders[2] = pz;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   void SetOrder() const override;
+
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the divergence of all shape functions of a *vector*
+       finite element in reference space at the given point @a ip. */
+   /** The size (#dof) of the result Vector @a divshape must be set in advance.
+    */
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+
+   ~NURBS_HDiv3DFiniteElement();
+};
+
+
+/** An arbitrary order H(curl)-conforming 2D NURBS element on a square
+    More details in the following paper:
+
+    [1] Annalisa Buffa, Giancarlo Sangalli, Rafael Vázquez
+    "Isogeometric analysis in electromagnetics: B-splines approximation."
+    Computer Methods in Applied Mechanics and Engineering (199) 1143-1152 */
+class NURBS_HCurl2DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, dshape_x, dshape_y, d2shape_x, d2shape_y;
+   mutable Vector shape1_x, shape1_y, dshape1_x, dshape1_y, d2shape1_x, d2shape1_y;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HCurl2DFiniteElement of order @a p
+   NURBS_HCurl2DFiniteElement(int p)
+      : VectorFiniteElement(2, Geometry::SQUARE, 2*(p + 1)*(p + 2), p,
+                            H_CURL,FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(p + 1), shape_y(p + 1), dshape_x(p + 1),
+        dshape_y(p + 1), d2shape_x(p + 1), d2shape_y(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), dshape1_x(p + 2),
+        dshape1_y(p + 2), d2shape1_x(p + 2), d2shape1_y(p + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = orders[1] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   /// Construct the NURBS_HCurl2DFiniteElement with x-order @a px and y-order @a py
+   NURBS_HCurl2DFiniteElement(int px, int py)
+      : VectorFiniteElement(2, Geometry::SQUARE,
+                            (px + 1)*(py + 2)+(px + 2)*(py + 1),
+                            std::max(px, py), H_CURL, FunctionSpace::Qk),
+        NURBSFiniteElement(2),
+        shape_x(px + 1), shape_y(py + 1), dshape_x(px + 1),
+        dshape_y(py + 1), d2shape_x(px + 1), d2shape_y(py + 1),
+        shape1_x(px + 2), shape1_y(py + 2), dshape1_x(px + 2),
+        dshape1_y(py + 2), d2shape1_x(px + 2), d2shape1_y(py + 2),
+        u(dof), du(dof,2)
+   {
+      orders[0] = px; orders[1] = py;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+   }
+
+   void SetOrder() const override;
+
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the curl of all shape functions of a *vector* finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a curl_shape contains the components
+       of the curl of one vector shape function. The size (#dof x CDim) of
+       @a curl_shape must be set in advance, where CDim = 3 for #dim = 3 and
+       CDim = 1 for #dim = 2. */
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
+
+   ~NURBS_HCurl2DFiniteElement();
+};
+
+
+/** An arbitrary order H(curl)-conforming 3D NURBS element on a cube
+    More details in the following paper:
+
+    [1] Annalisa Buffa, Giancarlo Sangalli, Rafael Vázquez
+    "Isogeometric analysis in electromagnetics: B-splines approximation."
+    Computer Methods in Applied Mechanics and Engineering (199) 1143-1152 */
+class NURBS_HCurl3DFiniteElement : public VectorFiniteElement,
+   public NURBSFiniteElement
+{
+protected:
+   mutable Vector shape_x, shape_y, shape_z;
+   mutable Vector dshape_x, dshape_y, dshape_z;
+   mutable Vector d2shape_x, d2shape_y, d2shape_z;
+   mutable Vector shape1_x, shape1_y, shape1_z;
+   mutable Vector dshape1_x, dshape1_y, dshape1_z;
+   mutable Vector d2shape1_x, d2shape1_y, d2shape1_z;
+   mutable Vector u;
+   mutable DenseMatrix du;
+   mutable Array <const KnotVector*> kv1;
+
+public:
+   /// Construct the NURBS_HCurl3DFiniteElement of order @a p
+   NURBS_HCurl3DFiniteElement(int p)
+      : VectorFiniteElement(3, Geometry::CUBE, 3*(p + 1)*(p + 2)*(p + 2), p,
+                            H_CURL,FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(p + 1), shape_y(p + 1), shape_z(p + 1),
+        dshape_x(p + 1), dshape_y(p + 1), dshape_z(p + 1),
+        d2shape_x(p + 1), d2shape_y(p + 1), d2shape_z(p + 1),
+        shape1_x(p + 2), shape1_y(p + 2), shape1_z(p + 2),
+        dshape1_x(p + 2), dshape1_y(p + 2),dshape1_z(p + 2),
+        d2shape1_x(p + 2), d2shape1_y(p + 2), d2shape1_z(p + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = orders[1] = orders[2] = p;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   /// Construct the NURBS_HCurl3DFiniteElement with x-order @a px, y-order @a py and z-order @a pz
+   NURBS_HCurl3DFiniteElement(int px, int py, int pz)
+      : VectorFiniteElement(3, Geometry::CUBE,
+                            (px + 1)*(py + 2)*(pz + 2) +
+                            (px + 2)*(py + 1)*(pz + 2) +
+                            (px + 2)*(py + 2)*(pz + 1),
+                            std::max(std::max(px, py), pz), H_CURL, FunctionSpace::Qk),
+        NURBSFiniteElement(3),
+        shape_x(px + 1), shape_y(py + 1), shape_z(pz + 1),
+        dshape_x(px + 1), dshape_y(py + 1), dshape_z(pz + 1),
+        d2shape_x(px + 1), d2shape_y(py + 1), d2shape_z(pz + 1),
+        shape1_x(px + 2), shape1_y(py + 2), shape1_z(pz + 2),
+        dshape1_x(px + 2), dshape1_y(py + 2),dshape1_z(pz + 2),
+        d2shape1_x(px + 2), d2shape1_y(py + 2), d2shape1_z(pz + 2),
+        u(dof), du(dof,3)
+   {
+      orders[0] = px; orders[1] = py; orders[2] = pz;
+      kv1.SetSize(dim);
+      kv1[0] = nullptr;
+      kv1[1] = nullptr;
+      kv1[2] = nullptr;
+   }
+
+   void SetOrder() const override;
+
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the values of all shape functions of a *vector* finite
+       element in physical space at the point described by @a Trans. */
+   /** Each row of the result DenseMatrix @a shape contains the components of
+       one vector shape function. The size (#dof x SDim) of @a shape must be set
+       in advance, where SDim >= #dim is the physical space dimension as
+       described by @a Trans. */
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;
+
+   /** @brief Evaluate the curl of all shape functions of a *vector* finite
+       element in reference space at the given point @a ip. */
+   /** Each row of the result DenseMatrix @a curl_shape contains the components
+       of the curl of one vector shape function. The size (#dof x CDim) of
+       @a curl_shape must be set in advance, where CDim = 3 for #dim = 3 and
+       CDim = 1 for #dim = 2. */
+   void CalcCurlShape(const IntegrationPoint &ip,
+                      DenseMatrix &curl_shape) const override;
+
+   ~NURBS_HCurl3DFiniteElement();
 };

 } // namespace mfem
@@ -34,31 +34,31 @@ public:
      ScalarFiniteElement(D, G, Do, O, F)
   { }

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { ScalarLocalInterpolation(Trans, I, *this); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { ScalarLocalL2Restriction(Trans, R, *this); }

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { CheckScalarFE(fe).ScalarLocalInterpolation(Trans, I, *this); }

   using FiniteElement::Project;

   // Low-order monotone "projection" (actually it is not a projection): the
   // dofs are set to be the Coefficient values at the nodes.
-   virtual void Project(Coefficient &coeff,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(Coefficient &coeff,
+                ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void Project (VectorCoefficient &vc,
-                         ElementTransformation &Trans, Vector &dofs) const;
+   void Project (VectorCoefficient &vc,
+                 ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override;
 };


@@ -88,17 +88,17 @@ class BiQuadPos2DFiniteElement : public PositiveFiniteElement
 public:
   /// Construct the BiQuadPos2DFiniteElement
   BiQuadPos2DFiniteElement();
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override;
   using FiniteElement::Project;
-   virtual void Project(Coefficient &coeff, ElementTransformation &Trans,
-                        Vector &dofs) const;
-   virtual void Project(VectorCoefficient &vc, ElementTransformation &Trans,
-                        Vector &dofs) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const
+   void Project(Coefficient &coeff, ElementTransformation &Trans,
+                Vector &dofs) const override;
+   void Project(VectorCoefficient &vc, ElementTransformation &Trans,
+                Vector &dofs) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override
   { dofs = 0.; dofs(vertex) = 1.; }
 };

@@ -109,9 +109,9 @@ class QuadPos1DFiniteElement : public PositiveFiniteElement
 public:
   /// Construct the QuadPos1DFiniteElement
   QuadPos1DFiniteElement();
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };


@@ -131,10 +131,10 @@ private:
 public:
   /// Construct the H1Pos_SegmentElement of order @a p
   H1Pos_SegmentElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -150,10 +150,10 @@ private:
 public:
   /// Construct the H1Pos_QuadrilateralElement of order @a p
   H1Pos_QuadrilateralElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -169,10 +169,10 @@ private:
 public:
   /// Construct the H1Pos_HexahedronElement of order @a p
   H1Pos_HexahedronElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -198,9 +198,9 @@ public:
   static void CalcDShape(const int p, const real_t x, const real_t y,
                          real_t *dshape_1d, real_t *dshape);

-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };


@@ -227,9 +227,9 @@ public:
   static void CalcDShape(const int p, const real_t x, const real_t y,
                          const real_t z, real_t *dshape_1d, real_t *dshape);

-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };


@@ -250,9 +250,9 @@ public:
   /// Construct the H1Pos_WedgeElement of order @a p
   H1Pos_WedgeElement(const int p);

-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };


@@ -267,10 +267,10 @@ private:
 public:
   /// Construct the L2Pos_SegmentElement of order @a p
   L2Pos_SegmentElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -285,10 +285,10 @@ private:
 public:
   /// Construct the L2Pos_QuadrilateralElement of order @a p
   L2Pos_QuadrilateralElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -303,10 +303,10 @@ private:
 public:
   /// Construct the L2Pos_HexahedronElement of order @a p
   L2Pos_HexahedronElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -321,10 +321,10 @@ private:
 public:
   /// Construct the L2Pos_TriangleElement of order @a p
   L2Pos_TriangleElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -340,10 +340,10 @@ private:
 public:
   /// Construct the L2Pos_TetrahedronElement of order @a p
   L2Pos_TetrahedronElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void ProjectDelta(int vertex, Vector &dofs) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void ProjectDelta(int vertex, Vector &dofs) const override;
 };


@@ -364,9 +364,9 @@ public:
   /// Construct the L2Pos_WedgeElement of order @a p
   L2Pos_WedgeElement(const int p);

-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
 };

 } // namespace mfem
@@ -38,51 +38,52 @@ public:
   RT_QuadrilateralElement(const int p,
                           const int cb_type = BasisType::GaussLobatto,
                           const int ob_type = BasisType::GaussLegendre);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_RT(Trans, shape); }
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   {
      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
      else { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_RT(nk, dof2nk, fe, Trans, I); }
   // Gradient + rotation = Curl: H1 -> H(div)
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
   // Curl = Gradient + rotation: H1 -> H(div)
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }

-   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+   void GetFaceMap(const int face_id, Array<int> &face_map) const override;

 protected:
   void ProjectIntegrated(VectorCoefficient &vc, ElementTransformation &Trans,
@@ -109,48 +110,49 @@ public:
                        const int cb_type = BasisType::GaussLobatto,
                        const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_RT(Trans, shape); }
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   {
      if (obasis1d.IsIntegratedType()) { ProjectIntegrated(vc, Trans, dofs); }
      else { Project_RT(nk, dof2nk, vc, Trans, dofs); }
   }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_RT(nk, dof2nk, fe, Trans, I); }
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }

   /// @brief Return the mapping from lexicographically ordered face DOFs to
   /// lexicographically ordered element DOFs corresponding to local face
   /// @a face_id.
-   virtual void GetFaceMap(const int face_id, Array<int> &face_map) const;
+   void GetFaceMap(const int face_id, Array<int> &face_map) const override;

 protected:
   void ProjectIntegrated(VectorCoefficient &vc,
@@ -176,45 +178,46 @@ class RT_TriangleElement : public VectorFiniteElement
 public:
   /// Construct the RT_TriangleElement of order @a p
   RT_TriangleElement(const int p);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_RT(Trans, shape); }
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_RT(nk, dof2nk, fe, Trans, I); }
   // Gradient + rotation = Curl: H1 -> H(div)
-   virtual void ProjectGrad(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &grad) const
+   void ProjectGrad(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &grad) const override
   { ProjectGrad_RT(nk, dof2nk, fe, Trans, grad); }
   // Curl = Gradient + rotation: H1 -> H(div)
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectGrad_RT(nk, dof2nk, fe, Trans, curl); }
 };

@@ -236,39 +239,40 @@ class RT_TetrahedronElement : public VectorFiniteElement
 public:
   /// Construct the RT_TetrahedronElement of order @a p
   RT_TetrahedronElement(const int p);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_RT(Trans, shape); }
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
-                                 Vector &dofs) const
+   void ProjectFromNodes(Vector &vc, ElementTransformation &Trans,
+                         Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_RT(nk, dof2nk, fe, Trans, I); }
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 };

@@ -296,36 +300,37 @@ class RT_WedgeElement : public VectorFiniteElement

 public:
   RT_WedgeElement(const int p);
-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override
   { CalcVShape_RT(Trans, shape); }
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation_RT(*this, nk, dof2nk, Trans, I); }
-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { LocalRestriction_RT(nk, dof2nk, Trans, R); }
-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation_RT(CheckVectorFE(fe), nk, dof2nk, Trans, I); }
   using FiniteElement::Project;
-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override
   { Project_RT(nk, dof2nk, vc, Trans, dofs); }
-   virtual void ProjectMatrixCoefficient(
-      MatrixCoefficient &mc, ElementTransformation &T, Vector &dofs) const
+   void ProjectMatrixCoefficient(MatrixCoefficient &mc,
+                                 ElementTransformation &T,
+                                 Vector &dofs) const override
   { ProjectMatrixCoefficient_RT(nk, dof2nk, mc, T, dofs); }
-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override
   { Project_RT(nk, dof2nk, fe, Trans, I); }
-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override
   { ProjectCurl_RT(nk, dof2nk, fe, Trans, curl); }
 };

@@ -353,27 +358,27 @@ public:
                         const int cb_type = BasisType::GaussLobatto,
                         const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void Project(const FiniteElement &fe,
-                        ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe,
+                ElementTransformation &Trans,
+                DenseMatrix &I) const override;

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const;
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override;
 };


@@ -401,26 +406,26 @@ public:
   RT_R2D_SegmentElement(const int p,
                         const int ob_type = BasisType::GaussLegendre);

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &div_shape) const;
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &div_shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation(*this, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override
   { MFEM_ABORT("method is not overloaded"); }

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }
 };

@@ -440,32 +445,32 @@ private:
 public:
   using FiniteElement::CalcVShape;

-   virtual void CalcVShape(ElementTransformation &Trans,
-                           DenseMatrix &shape) const;
+   void CalcVShape(ElementTransformation &Trans,
+                   DenseMatrix &shape) const override;

-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override
   { LocalInterpolation(*this, Trans, I); }

-   virtual void GetLocalRestriction(ElementTransformation &Trans,
-                                    DenseMatrix &R) const;
+   void GetLocalRestriction(ElementTransformation &Trans,
+                            DenseMatrix &R) const override;

-   virtual void GetTransferMatrix(const FiniteElement &fe,
-                                  ElementTransformation &Trans,
-                                  DenseMatrix &I) const
+   void GetTransferMatrix(const FiniteElement &fe,
+                          ElementTransformation &Trans,
+                          DenseMatrix &I) const override
   { LocalInterpolation(CheckVectorFE(fe), Trans, I); }

   using FiniteElement::Project;

-   virtual void Project(VectorCoefficient &vc,
-                        ElementTransformation &Trans, Vector &dofs) const;
+   void Project(VectorCoefficient &vc,
+                ElementTransformation &Trans, Vector &dofs) const override;

-   virtual void Project(const FiniteElement &fe, ElementTransformation &Trans,
-                        DenseMatrix &I) const;
+   void Project(const FiniteElement &fe, ElementTransformation &Trans,
+                DenseMatrix &I) const override;

-   virtual void ProjectCurl(const FiniteElement &fe,
-                            ElementTransformation &Trans,
-                            DenseMatrix &curl) const;
+   void ProjectCurl(const FiniteElement &fe,
+                    ElementTransformation &Trans,
+                    DenseMatrix &curl) const override;
 };

 /// Arbitrary order Raviart-Thomas 3D elements in 2D on a triangle
@@ -489,11 +494,11 @@ public:

   using RT_R2D_FiniteElement::CalcVShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;

-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
 };

 /// Arbitrary order Raviart-Thomas 3D elements in 2D on a square
@@ -518,10 +523,10 @@ public:

   using RT_R2D_FiniteElement::CalcVShape;

-   virtual void CalcVShape(const IntegrationPoint &ip,
-                           DenseMatrix &shape) const;
-   virtual void CalcDivShape(const IntegrationPoint &ip,
-                             Vector &divshape) const;
+   void CalcVShape(const IntegrationPoint &ip,
+                   DenseMatrix &shape) const override;
+   void CalcDivShape(const IntegrationPoint &ip,
+                     Vector &divshape) const override;
 };


@@ -23,11 +23,11 @@ class H1Ser_QuadrilateralElement : public ScalarFiniteElement
 public:
   /// Construct the H1Ser_QuadrilateralElement of order @a p
   H1Ser_QuadrilateralElement(const int p);
-   virtual void CalcShape(const IntegrationPoint &ip, Vector &shape) const;
-   virtual void CalcDShape(const IntegrationPoint &ip,
-                           DenseMatrix &dshape) const;
-   virtual void GetLocalInterpolation(ElementTransformation &Trans,
-                                      DenseMatrix &I) const;
+   void CalcShape(const IntegrationPoint &ip, Vector &shape) const override;
+   void CalcDShape(const IntegrationPoint &ip,
+                   DenseMatrix &dshape) const override;
+   void GetLocalInterpolation(ElementTransformation &Trans,
+                              DenseMatrix &I) const override;
   using FiniteElement::Project;
 };

@@ -344,6 +344,32 @@ FiniteElementCollection *FiniteElementCollection::New(const char *name)
   {
      fec = new Local_FECollection(name + 6);
   }
+   else if (!strncmp(name, "NURBS_HDiv", 10))
+   {
+      if (name[10] != '\0')
+      {
+         // "NURBS" + "number" --> fixed order nurbs collection
+         fec = new NURBS_HDivFECollection(atoi(name + 10));
+      }
+      else
+      {
+         // "NURBS" --> variable order nurbs collection
+         fec = new NURBS_HDivFECollection();
+      }
+   }
+   else if (!strncmp(name, "NURBS_HCurl", 11))
+   {
+      if (name[11] != '\0')
+      {
+         // "NURBS" + "number" --> fixed order nurbs collection
+         fec = new NURBS_HCurlFECollection(atoi(name + 11));
+      }
+      else
+      {
+         // "NURBS" --> variable order nurbs collection
+         fec = new NURBS_HCurlFECollection();
+      }
+   }
   else if (!strncmp(name, "NURBS", 5))
   {
      if (name[5] != '\0')
@@ -3533,4 +3559,192 @@ FiniteElementCollection *NURBSFECollection::GetTraceCollection() const
   return NULL;
 }

+
+NURBS_HDivFECollection::NURBS_HDivFECollection(int Order, const int dim)
+   : NURBSFECollection((Order == VariableOrder) ? 1 : Order)
+{
+   const int order = (Order == VariableOrder) ? 1 : Order;
+
+   SegmentFE       = new NURBS1DFiniteElement(order);
+   QuadrilateralFE = new NURBS2DFiniteElement(order);
+
+   QuadrilateralVFE  = new NURBS_HDiv2DFiniteElement(order);
+   ParallelepipedVFE = new NURBS_HDiv3DFiniteElement(order);
+
+   if (dim != -1) { SetDim(dim); }
+   SetOrder(Order);
+}
+
+void NURBS_HDivFECollection::SetDim(int dim)
+{
+   if (dim == 2)
+   {
+      sFE = SegmentFE;
+      qFE = QuadrilateralVFE;
+      hFE = nullptr;
+   }
+   else if (dim == 3)
+   {
+      sFE = nullptr;
+      qFE = QuadrilateralFE;
+      hFE = ParallelepipedVFE;
+   }
+   else
+   {
+      mfem::err<<"Dimension = "<<dim<<endl;
+      mfem_error ("NURBS_HDivFECollection: wrong dimension!");
+   }
+}
+
+NURBS_HDivFECollection::~NURBS_HDivFECollection()
+{
+   delete SegmentFE;
+   delete QuadrilateralFE;
+   delete QuadrilateralVFE;
+   delete ParallelepipedVFE;
+}
+
+const FiniteElement *
+NURBS_HDivFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   switch (GeomType)
+   {
+      case Geometry::SEGMENT:     return sFE;
+      case Geometry::SQUARE:      return qFE;
+      case Geometry::CUBE:        return hFE;
+      default:
+         if (error_mode == RETURN_NULL) { return nullptr; }
+         mfem_error ("NURBS_HDivFECollection: unknown geometry type.");
+   }
+   return QuadrilateralFE; // Make some compilers happy
+}
+
+void NURBS_HDivFECollection::SetOrder(int Order) const
+{
+   mOrder = Order;
+   if (Order != VariableOrder)
+   {
+      snprintf(name, 16, "NURBS_HDiv%i", Order);
+   }
+   else
+   {
+      snprintf(name, 16, "NURBS_HDiv");
+   }
+}
+
+int NURBS_HDivFECollection::DofForGeometry(Geometry::Type GeomType) const
+{
+   mfem_error("NURBS_HDivFECollection::DofForGeometry");
+   return 0; // Make some compilers happy
+}
+
+const int *NURBS_HDivFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType,
+   int Or) const
+{
+   mfem_error("NURBS_HDivFECollection::DofOrderForOrientation");
+   return NULL;
+}
+
+FiniteElementCollection *NURBS_HDivFECollection::GetTraceCollection() const
+{
+   MFEM_ABORT("NURBS finite elements can not be statically condensed!");
+   return NULL;
+}
+
+NURBS_HCurlFECollection::NURBS_HCurlFECollection(int Order, const int dim)
+   : NURBSFECollection((Order == VariableOrder) ? 1 : Order)
+{
+   const int order = (Order == VariableOrder) ? 1 : Order;
+
+   SegmentFE       = new NURBS1DFiniteElement(order+1);
+   QuadrilateralFE = new NURBS2DFiniteElement(order+1);
+
+   QuadrilateralVFE  = new NURBS_HCurl2DFiniteElement(order);
+   ParallelepipedVFE = new NURBS_HCurl3DFiniteElement(order);
+   if (dim != -1) { SetDim(dim); }
+   SetOrder(Order);
+}
+
+void NURBS_HCurlFECollection::SetDim(int dim)
+{
+   if (dim == 2)
+   {
+      sFE = SegmentFE;
+      qFE = QuadrilateralVFE;
+      hFE = nullptr;
+   }
+   else if (dim == 3)
+   {
+      sFE = nullptr;
+      qFE = QuadrilateralFE;
+      hFE = ParallelepipedVFE;
+   }
+   else
+   {
+      mfem::err<<"Dimension = "<<dim<<endl;
+      mfem_error ("NURBS_HCurlFECollection: wrong dimension!");
+   }
+}
+
+
+
+NURBS_HCurlFECollection::~NURBS_HCurlFECollection()
+{
+   delete SegmentFE;
+   delete QuadrilateralFE;
+   delete QuadrilateralVFE;
+   delete ParallelepipedVFE;
+}
+
+const FiniteElement *
+NURBS_HCurlFECollection::FiniteElementForGeometry(Geometry::Type GeomType) const
+{
+   switch (GeomType)
+   {
+      case Geometry::SEGMENT:     return sFE;
+      case Geometry::SQUARE:      return qFE;
+      case Geometry::CUBE:        return hFE;
+      default:
+         if (error_mode == RETURN_NULL) { return nullptr; }
+         mfem_error ("NURBS_HCurlFECollection: unknown geometry type.");
+   }
+   return QuadrilateralFE; // Make some compilers happy
+}
+
+void NURBS_HCurlFECollection::SetOrder(int Order) const
+{
+   mOrder = Order;
+   if (Order != VariableOrder)
+   {
+      snprintf(name, 16, "NURBS_HCurl%i", Order);
+   }
+   else
+   {
+      snprintf(name, 16, "NURBS_HCurl");
+   }
+}
+
+int NURBS_HCurlFECollection::DofForGeometry(Geometry::Type GeomType) const
+{
+   mfem_error("NURBS_HCurlFECollection::DofForGeometry");
+   return 0; // Make some compilers happy
+}
+
+const int *NURBS_HCurlFECollection::DofOrderForOrientation(
+   Geometry::Type GeomType,
+   int Or) const
+{
+   mfem_error("NURBS_HCurlFECollection::DofOrderForOrientation");
+   return NULL;
+}
+
+FiniteElementCollection *NURBS_HCurlFECollection::GetTraceCollection() const
+{
+   MFEM_ABORT("NURBS finite elements can not be statically condensed!");
+   return NULL;
+}
+
+
+
 }
@@ -680,8 +680,8 @@ public:
 /// Arbitrary order non-uniform rational B-splines (NURBS) finite elements.
 class NURBSFECollection : public FiniteElementCollection
 {
-private:
-   PointFiniteElement   *PointFE;
+protected:
+   PointFiniteElement *PointFE;
   NURBS1DFiniteElement *SegmentFE;
   NURBS2DFiniteElement *QuadrilateralFE;
   NURBS3DFiniteElement *ParallelepipedFE;
@@ -701,13 +701,15 @@ public:
      order, or VariableOrder (default). */
   explicit NURBSFECollection(int Order = VariableOrder);

-   void Reset() const
+   virtual void Reset() const
   {
      SegmentFE->Reset();
      QuadrilateralFE->Reset();
      ParallelepipedFE->Reset();
   }

+   virtual void SetDim(const int dim) {};
+
   /** @brief Get the order of the NURBS collection: either a positive number,
       when using fixed order, or VariableOrder. */
   /** @note Not to be confused with FiniteElementCollection::GetOrder(). */
@@ -715,7 +717,7 @@ public:

   /** @brief Set the order and the name, based on the given @a Order: either a
       positive number for fixed order, or VariableOrder. */
-   void SetOrder(int Order) const;
+   virtual void SetOrder(int Order) const;

   const FiniteElement *
   FiniteElementForGeometry(Geometry::Type GeomType) const override;
@@ -734,6 +736,109 @@ public:
   virtual ~NURBSFECollection();
 };

+/// Arbitrary order H(div) NURBS finite elements.
+class NURBS_HDivFECollection : public NURBSFECollection
+{
+private:
+
+   NURBS1DFiniteElement *SegmentFE;
+   NURBS2DFiniteElement *QuadrilateralFE;
+
+   NURBS_HDiv2DFiniteElement *QuadrilateralVFE;
+   NURBS_HDiv3DFiniteElement *ParallelepipedVFE;
+
+   FiniteElement *sFE;
+   FiniteElement *qFE;
+   FiniteElement *hFE;
+
+public:
+
+   /** @brief The parameter @a Order must be either a positive number, for fixed
+      order, or VariableOrder (default). */
+   explicit NURBS_HDivFECollection(int Order = VariableOrder, const int vdim = -1);
+
+   void Reset() const override
+   {
+      SegmentFE->Reset();
+      QuadrilateralFE->Reset();
+      QuadrilateralVFE->Reset();
+      ParallelepipedVFE->Reset();
+   }
+
+   void SetDim(const int dim) override;
+
+   /** @brief Set the order and the name, based on the given @a Order: either a
+       positive number for fixed order, or VariableOrder. */
+   void SetOrder(int Order) const override;
+
+   const FiniteElement *
+   FiniteElementForGeometry(Geometry::Type GeomType) const override;
+
+   int DofForGeometry(Geometry::Type GeomType) const override;
+
+   const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                     int Or) const override;
+
+   const char *Name() const override { return name; }
+
+   int GetContType() const override { return CONTINUOUS; }
+
+   FiniteElementCollection *GetTraceCollection() const override;
+
+   virtual ~NURBS_HDivFECollection();
+};
+
+/// Arbitrary order H(curl) NURBS finite elements.
+class NURBS_HCurlFECollection : public NURBSFECollection
+{
+private:
+   NURBS1DFiniteElement *SegmentFE;
+   NURBS2DFiniteElement *QuadrilateralFE;
+
+   NURBS_HCurl2DFiniteElement *QuadrilateralVFE;
+   NURBS_HCurl3DFiniteElement *ParallelepipedVFE;
+
+   FiniteElement *sFE;
+   FiniteElement *qFE;
+   FiniteElement *hFE;
+public:
+
+   /** @brief The parameter @a Order must be either a positive number, for fixed
+      order, or VariableOrder (default). */
+   explicit NURBS_HCurlFECollection(int Order = VariableOrder,
+                                    const int vdim = -1);
+
+   void Reset() const override
+   {
+      SegmentFE->Reset();
+      QuadrilateralFE->Reset();
+      QuadrilateralVFE->Reset();
+      ParallelepipedVFE->Reset();
+   }
+
+   void SetDim(const int dim) override;
+
+   /** @brief Set the order and the name, based on the given @a Order: either a
+       positive number for fixed order, or VariableOrder. */
+   void SetOrder(int Order) const override;
+
+   const FiniteElement *
+   FiniteElementForGeometry(Geometry::Type GeomType) const override;
+
+   int DofForGeometry(Geometry::Type GeomType) const override;
+
+   const int *DofOrderForOrientation(Geometry::Type GeomType,
+                                     int Or) const override;
+
+   const char *Name() const override { return name; }
+
+   int GetContType() const override { return CONTINUOUS; }
+
+   FiniteElementCollection *GetTraceCollection() const override;
+
+   virtual ~NURBS_HCurlFECollection();
+};
+
 /// Piecewise-(bi/tri)linear continuous finite elements.
 class LinearFECollection : public FiniteElementCollection
 {
--- a/Show More
+++ b/Show More