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Volume 32, Issue 5
The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle

Ang Li, Hongtao Yang, Yonghai Li & Guangwei Yuan

DOI: 10.4208/cicp.OA-2022-0130

Commun. Comput. Phys., 32 (2022), pp. 1437-1473.

Published online: 2023-01

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  • 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.

  • Keywords

Diffusion equations, finite volume element, flux-correct, maximum principle.

  • AMS Subject Headings

65N08

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{CiCP-32-1437, author = {Li , AngYang , HongtaoLi , Yonghai and Yuan , Guangwei}, title = {The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle}, journal = {Communications in Computational Physics}, year = {2023}, volume = {32}, number = {5}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2022-0130}, url = {http://global-sci.org/intro/article_detail/cicp/21369.html} }
TY - JOUR T1 - The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle AU - Li , Ang AU - Yang , Hongtao AU - Li , Yonghai AU - Yuan , Guangwei JO - Communications in Computational Physics VL - 5 SP - 1437 EP - 1473 PY - 2023 DA - 2023/01 SN - 32 DO - http://doi.org/10.4208/cicp.OA-2022-0130 UR - https://global-sci.org/intro/article_detail/cicp/21369.html KW - Diffusion equations, finite volume element, flux-correct, maximum principle. AB -

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.

Li , AngYang , HongtaoLi , Yonghai and Yuan , Guangwei. (2023). The Corrected Finite Volume Element Methods for Diffusion Equations Satisfying Discrete Extremum Principle. Communications in Computational Physics. 32 (5). 1437-1473. doi:10.4208/cicp.OA-2022-0130
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