A stabilized linearity-preserving scheme for the heterogeneous and anisotropic diffusion problems on polygonal meshes

Authors:
Jiming Wu;Zhiming Gao;Zihuan Dai
Affiliations:
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China;Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China;Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, PR China
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

In this paper a stabilized discretization scheme for the heterogeneous and anisotropic diffusion problems is proposed on general, possibly nonconforming polygonal meshes. The unknowns are the values at the cell center and the scheme relies on linearity-preserving criterion and the use of the so-called harmonic averaging points located at the interface of heterogeneity. The stability result and error estimate both in H"1 norm are obtained under quite general and standard assumptions on polygonal meshes. The experiment results on a number of different meshes show that the scheme maintains optimal convergence rates in both L"2 and H"1 norms.