A linearity-preserving cell-centered scheme for the anisotropic diffusion equations

Abstract

In this paper a cell-centered discretization scheme for the heterogeneous and anisotropic diffusion problems is proposed on general polygonal meshes. The unknowns are the values at the cell center and the scheme relies on linearitypreserving criterion and the use of the harmonic averaging points located at the interface of heterogeneity. Numerical results show that our scheme is robust, and the optimal convergence rates are verified on general distorted meshes in case that the diffusion tensor is taken to be anisotropic, at times discontinuous.