Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems. Issue 6 (December 2014)

• Record Type: Journal Article
• Authors: Chen, Xingding; Yuan, Guangwei; Yu, Yunlong
• Is Part Of: Advances in applied mathematics and mechanics. Volume 6:Issue 6(2014)
• Page Start: 849
• Page End: 866
• Publication Date: 2014-12
• Subjects: 65M12, -- 65M60; Discrete maximum principle, -- finite element scheme, -- repair technique, -- anisotropic diffusion problems; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2013.m445
• Languages: English
• ISSNs: 2070-0733

Abstract

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.