Article · Wikipedia archive · Last revised Jun 23, 2026

MFEM

MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license.

Last revised
Jun 23, 2026
Read time
≈ 2 min
Length
415 w
Citations
7
Source
Wikipedia ↗
MFEM
Stable release
4.9 / December 11, 2025 (2025-12-11)
Written inC++
Operating systemLinux, MacOS, Microsoft Windows
TypeFinite element analysis
LicenseBSD
Websitemfem.org
Repositoryhttps://github.com/mfem/mfem

MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license.1

The library consists of C++ classes that serve as building blocks for developing finite element solvers applicable to problems of fluid dynamics,2 structural mechanics,3 electromagnetics,4 radiative transfer5 and many other.

Features

Some of the features of MFEM include6

  • Arbitrary high order finite elements with curved boundaries.
  • H1, H(curl) and H(div) conforming, discontinuous (L2), and NURBS finite element spaces.
  • Local mesh refinement, both conforming (simplex meshes) and non-conforming (quadrilateral/hexahedral meshes).
  • Highly scalable MPI-based parallelism and GPU acceleration.7
  • Wide variety of finite element discretization approaches, including Galerkin, discontinuous Galerkin, mixed, high-order and isogeometric analysis methods.
  • Tight integration with the Hypre parallel linear algebra library.
  • Many built-in solvers and interfaces to external libraries such as PETSc, SuiteSparse, Gmsh, etc.
  • Accurate and flexible visualization with VisIt and ParaView.
  • Lightweight design and conservative use of C++ templating.
  • Documentation in the form of examples and mini-applications.
See also

See also

References

References

  1. Auten, Holly. "The High Value of Open-Source Software" (PDF). Science & Technology Review. January/February 2018: 5–11.
  2. Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N. (2018). "High-Order Multi-Material ALE Hydrodynamics". SIAM Journal on Scientific Computing. 40 (1): B32–B58. Bibcode:2018SJSC...40B..32A. doi:10.1137/17M1116453. OSTI 1474269.
  3. White, D. A.; Stowell, M. L.; Tortorelli, D. A. (2018). "Topological optimization of structures using Fourier representations". Structural and Multidisciplinary Optimization. 58 (3): 1205–1220. doi:10.1007/s00158-018-1962-y. OSTI 1479078. S2CID 126093513.
  4. Shiraiwa, S.; Wright, J. C.; Bonoli, P. T.; Kolev, T.; Stowell, M. (23 October 2017). "RF wave simulation for cold edge plasmas using the MFEM library". EPJ Web of Conferences. 157: 03048. Bibcode:2017EPJWC.15703048S. doi:10.1051/epjconf/201715703048. hdl:1721.1/113307.
  5. Holec, M.; Limpouch, J.; Liska, R.; Weber, S. (10 April 2017). "High-order discontinuous Galerkin nonlocal transport and energy equations scheme for radiation hydrodynamics". Numerical Methods in Fluids. 83 (10): 779–797. Bibcode:2017IJNMF..83..779H. doi:10.1002/fld.4288. S2CID 125947931.
  6. "MFEM Finite Element Discretization Library".
  7. "MFEM video: Advanced simulation algorithms for HPC applications". YouTube. 24 June 2020.
External links