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                Finite Element Discretization Library
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MFEM is a modular parallel C++ library for finite element methods. Its goal is to enable high-performance scalable finite element discretization research and application development on a wide variety of platforms, ranging from laptops to supercomputers.

We welcome contributions and feedback from the community. Please see the file for additional details about our development process.

  • For building instructions, see the file INSTALL, or type "make help".

  • Copyright and licensing information can be found in files LICENSE and NOTICE.

  • The best starting point for new users interested in MFEM's features is to review the examples and miniapps at

  • Instructions for learning with Docker are in config/docker.

Conceptually, MFEM can be viewed as a finite element toolbox that provides the building blocks for developing finite element algorithms in a manner similar to that of MATLAB for linear algebra methods. In particular, MFEM provides support for arbitrary high-order H1-conforming, discontinuous (L2), H(div)-conforming, H(curl)-conforming and NURBS finite element spaces in 2D and 3D, as well as many bilinear, linear and nonlinear forms defined on them. It enables the quick prototyping of various finite element discretizations, including Galerkin methods, mixed finite elements, Discontinuous Galerkin (DG), isogeometric analysis, hybridization and Discontinuous Petrov-Galerkin (DPG) approaches.

MFEM includes classes for dealing with a wide range of mesh types: triangular, quadrilateral, tetrahedral and hexahedral, as well as surface and topologically periodical meshes. It has general support for mesh refinement, including local conforming and non-conforming (AMR) adaptive refinement. Arbitrary element transformations, allowing for high-order mesh elements with curved boundaries, are also supported.

When used as a "finite element to linear algebra translator", MFEM can take a problem described in terms of finite element-type objects, and produce the corresponding linear algebra vectors and fully or partially assembled operators, e.g. in the form of global sparse matrices or matrix-free operators. The library includes simple smoothers and Krylov solvers, such as PCG, MINRES and GMRES, as well as support for sequential sparse direct solvers from the SuiteSparse library. Nonlinear solvers (the Newton method), eigensolvers (LOBPCG), and several explicit and implicit Runge-Kutta time integrators are also available.

MFEM supports MPI-based parallelism throughout the library, and can readily be used as a scalable unstructured finite element problem generator. Starting with version 4.0, MFEM offers support for GPU acceleration, and programming models, such as CUDA, HIP, OCCA, RAJA and OpenMP. MFEM-based applications require minimal changes to switch from a serial to a highly-performant MPI-parallel version of the code, where they can take advantage of the integrated linear solvers from the hypre library. Comprehensive support for other external packages, e.g. PETSc, SUNDIALS and libCEED is also included, giving access to additional linear and nonlinear solvers, preconditioners, time integrators, etc.

For examples of using MFEM, see the examples/ and miniapps/ directories, as well as the OpenGL visualization tool GLVis which is available at


MFEM is distributed under the terms of the BSD-3 license. All new contributions must be made under this license. See LICENSE and NOTICE for details.

SPDX-License-Identifier: BSD-3-Clause
LLNL Release Number: LLNL-CODE-806117
DOI: 10.11578/dc.20171025.1248