The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle
Year: 2022
Author: Ang Li, Hongtao Yang, Yonghai Li, Guangwei Yuan
Communications in Computational Physics, Vol. 32 (2022), Iss. 5 : pp. 1437–1473
Abstract
In this paper, we correct the finite volume element methods for diffusion equations on general triangular and quadrilateral meshes. First, we decompose the numerical fluxes of original schemes into two parts, i.e., the principal part with a two-point flux structure and the defective part. And then with the help of local extremums, we transform the original numerical fluxes into nonlinear numerical fluxes, which can be expressed as a nonlinear combination of two-point fluxes. It is proved that the corrected schemes satisfy the discrete strong extremum principle without restrictions on the diffusion coefficient and meshes. Numerical results indicate that the corrected schemes not only satisfy the discrete strong extremum principle but also preserve the convergence order of the original finite volume element methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0130
Communications in Computational Physics, Vol. 32 (2022), Iss. 5 : pp. 1437–1473
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 37
Keywords: Diffusion equations finite volume element flux-correct maximum principle.