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Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems

Published online by Cambridge University Press:  03 June 2015

Xingding Chen ,
Guangwei Yuan  and
Yunlong Yu
Xingding Chen*
Affiliation:
Department of Mathematics, School of Science, Beijing Technology and Business University, Beijing 100048, China
Guangwei Yuan*
Affiliation:
LCP, Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
Yunlong Yu*
Affiliation:
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, China
*
Corresponding author. Email: chenxd@lsec.cc.ac.cn
Email: ygw8009@sina.com
Email: yyliapcm@hotmail.com
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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 cheaper than the local repair technique when the diffusion tensors are highly anisotropic.

Keywords

65M1265M60Discrete maximum principlefinite element schemerepair techniqueanisotropic diffusion problems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 6 , December 2014 , pp. 849 - 866
Copyright
Copyright © Global-Science Press 2014

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