An Efficient Implementation of Brezzi-Douglas-Marini (BDM) Mixed Finite Element Method in MATLAB

TL;DR

This paper introduces a MATLAB package implementing the BDM mixed finite element method for elliptic diffusion problems, emphasizing efficiency, ease of use, and adaptability for complex edge-based finite element spaces.

Contribution

The paper provides a simple, efficient MATLAB implementation of BDM mixed finite elements with detailed handling of edge ordering and basis functions, facilitating broader application.

Findings

The MATLAB package effectively solves elliptic diffusion problems.

The implementation is optimized for unstructured grids and edge-based finite element spaces.

Numerical examples demonstrate the package's accuracy and usability.

Abstract

In this paper, a MATLAB package bdm_mfem for a linear Brezzi-Douglas- Marini (BDM) mixed finite element method is provided for the numerical solution of elliptic diffusion problems with mixed boundary conditions on unstructured grids. BDM basis functions defined by standard barycentric coordinates are used in the paper. Local and global edge ordering are treated carefully. MATLAB build-in functions and vectorizations are used to guarantee the erectness of the programs. The package is simple and efficient, and can be easily adapted for more complicated edge-based finite element spaces. A numerical example is provided to illustrate the usage of the package.