Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

Abstract

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle. The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix. Numerical results are presented to verify the theoretical findings.