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Volume 6, Issue 6
Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems

Xingding Chen, Guangwei Yuan & Yunlong Yu

DOI: 10.4208/aamm.2013.m445

Adv. Appl. Math. Mech., 6 (2014), pp. 849-866.

Published online: 2014-06

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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 lower than the local repair technique when the diffusion tensors are highly anisotropic.

  • Keywords

Discrete maximum principle, finite element scheme, repair technique, anisotropic diffusion problems.

  • AMS Subject Headings

65M12, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-6-849, author = {Chen , XingdingYuan , Guangwei and Yu , Yunlong}, title = {Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2014}, volume = {6}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m445}, url = {http://global-sci.org/intro/article_detail/aamm/52.html} }
TY - JOUR T1 - Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems AU - Chen , Xingding AU - Yuan , Guangwei AU - Yu , Yunlong JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 849 EP - 866 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m445 UR - https://global-sci.org/intro/article_detail/aamm/52.html KW - Discrete maximum principle, finite element scheme, repair technique, anisotropic diffusion problems. AB -

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.

Chen , XingdingYuan , Guangwei and Yu , Yunlong. (2014). Discrete Maximum Principle Based on Repair Technique for Finite Element Scheme of Anisotropic Diffusion Problems. Advances in Applied Mathematics and Mechanics. 6 (6). 849-866. doi:10.4208/aamm.2013.m445
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