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

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.