MFEM: A modular finite element methods library

Robert Anderson, Julian Andrej, Andrew Barker, Jamie Bramwell, Jean Sylvain Camier, Jakub Cerveny, Veselin Dobrev, Yohann Dudouit, Ido Akkerman, More Authors

Research output: Contribution to journalArticleScientificpeer-review

92 Citations (Scopus)
197 Downloads (Pure)


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
Pages (from-to)42-74
JournalComputers and Mathematics with Applications
Publication statusPublished - 2021

Bibliographical note

Accepted Author Manuscript


  • Finite element methods
  • High-order methods
  • High-performance computing
  • Matrix-free algorithms
  • Numerical PDEs
  • Open-source scientific software


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