Volume 18, Issue 2
A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems

Commun. Comput. Phys., 18 (2015), pp. 297-320.

Published online: 2018-04

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• Abstract

In this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

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@Article{CiCP-18-297, author = {}, title = {A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {2}, pages = {297--320}, abstract = {

In this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.120914.311214a}, url = {http://global-sci.org/intro/article_detail/cicp/11029.html} }
TY - JOUR T1 - A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems JO - Communications in Computational Physics VL - 2 SP - 297 EP - 320 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.120914.311214a UR - https://global-sci.org/intro/article_detail/cicp/11029.html KW - AB -

In this paper, we are concerned with the constrained finite element method based on domain decomposition satisfying the discrete maximum principle for diffusion problems with discontinuous coefficients on distorted meshes. The basic idea of domain decomposition methods is used to deal with the discontinuous coefficients. To get the information on the interface, we generalize the traditional Neumann-Neumann method to the discontinuous diffusion tensors case. Then, the constrained finite element method is used in each subdomain. Comparing with the method of using the constrained finite element method on the global domain, the numerical experiments show that not only the convergence order is improved, but also the nonlinear iteration time is reduced remarkably in our method.

Xingding Chen & Guangwei Yuan. (2020). A Constrained Finite Element Method Based on Domain Decomposition Satisfying the Discrete Maximum Principle for Diffusion Problems. Communications in Computational Physics. 18 (2). 297-320. doi:10.4208/cicp.120914.311214a
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