An Efficient Implementation of Brezzi-Douglas-Marini (BDM) Mixed Finite Element Method in MATLAB
Provides a practical tool for researchers needing to solve elliptic PDEs with mixed boundary conditions using BDM elements, but the contribution is incremental as it applies existing methods to a new implementation.
The paper presents a MATLAB package for implementing the BDM mixed finite element method for elliptic diffusion problems, achieving efficient computation through vectorization and careful edge ordering.
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.