Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems
Year: 2014
Author: Xingding Chen, Guangwei Yuan, Yunlong Yu
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 6 : pp. 849–866
Abstract
In this paper, we construct a global repair technique for the finite element scheme of anisotropic diffusion equations to enforce the repaired solutions satisfying the discrete maximum principle. It is an extension of the existing local repair technique. Both of the repair techniques preserve the total energy and are easy to be implemented. The numerical experiments show that these repair techniques do not destroy the accuracy of the finite element scheme, and the computational cost of the global repair technique is lower than the local repair technique when the diffusion tensors are highly anisotropic.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.2013.m445
Advances in Applied Mathematics and Mechanics, Vol. 6 (2014), Iss. 6 : pp. 849–866
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Discrete maximum principle finite element scheme repair technique anisotropic diffusion problems.