A monotone nonlinear cell-centered finite element method for anisotropic diffusion problems

Abstract

We present a technique to correct the cell-centered finite element scheme [20] (FECC) for full anisotropic diffusion problems on general meshes, which provides a discrete maximum principle (DMP). The correction scheme, named monotone nonlinear cell centered finite element scheme (MNFECC), is cell-centered in the sense that the solution can be computed from cell unknowns of the general primal mesh. Moreover, its coercivity and convergence are proven in a rigorous theoretical framework. Numerical experiments show that the method is effective and accurate, and it satisfies the discrete maximum principle.

Keywords

• discrete maximum principle
• heterogeneous anisotropic diffusion
• general grid
• finite volume
• finite elements
• cell-centered scheme