MFEM: A modular finite element methods library

Robert Anderson, Julian Andrej, Andrew Barker, Jamie Bramwell, Jean Sylvain Camier, Jakub Cerveny, Veselin Dobrev, Yohann Dudouit, Aaron Fisher, Tzanio Kolev, Will Pazner, Mark Stowell, Vladimir Tomov, Ido Akkerman, Johann Dahm, David Medina, Stefano Zampini

Research output: Contribution to journalArticlepeer-review

157 Scopus citations


MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and emphasis on usability, portability, and high-performance computing efficiency. MFEM's goal is to provide application scientists with access to cutting-edge algorithms for high-order finite element meshing, discretizations and linear solvers, while enabling researchers to quickly and easily develop and test new algorithms in very general, fully unstructured, high-order, parallel and GPU-accelerated settings. In this paper we describe the underlying algorithms and finite element abstractions provided by MFEM, discuss the software implementation, and illustrate various applications of the library.
Original languageEnglish (US)
JournalComputers and Mathematics with Applications
StatePublished - Jul 11 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, LLNL-JRNL-795849.The MFEM project would not have been possible without the help and advice of Joachim Schöberl, Panayot Vassilevski, and all the contributors in the MFEM open-source community, see and MFEM has been supported by a number of U.S. Department of Energy (DOE) grants, including the Applied Math and SciDAC programs in the DOE Office of Science, and the ASC and LDRD programs in NNSA. MFEM is also a major participant in the co-design Center for Efficient Exascale Discretizations (CEED) in the DOE's Exascale Computing Project. This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.


Dive into the research topics of 'MFEM: A modular finite element methods library'. Together they form a unique fingerprint.

Cite this