Volume 9, Issue 4
Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

Congcong Xie & Xianliang Hu

Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 686-704.

Published online: 2016-09

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  • Abstract

A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Serveral numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh method costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.

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@Article{NMTMA-9-686, author = {}, title = {Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2016}, volume = {9}, number = {4}, pages = {686--704}, abstract = {

A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Serveral numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh method costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2016.m1229}, url = {http://global-sci.org/intro/article_detail/nmtma/12395.html} }
TY - JOUR T1 - Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 686 EP - 704 PY - 2016 DA - 2016/09 SN - 9 DO - http://doi.org/10.4208/nmtma.2016.m1229 UR - https://global-sci.org/intro/article_detail/nmtma/12395.html KW - AB -

A moving mesh method is proposed for solving reaction-diffusion equations. The finite element method is used to solving the partial different equation system, and an efficient scheme is applied to implement mesh moving. In the practical calculations, the moving mesh step and the problem equation solver are performed alternatively. Serveral numerical examples are presented, including the Gray-Scott, the Activator-Inhibitor and a case with a growing domain. It is illustrated numerically that the moving mesh method costs much lower, compared with the numerical schemes on a fixed mesh. Even in the case of complex pattern dynamics described by the reaction-diffusion systems, the adapted meshes can capture the details successfully.

Congcong Xie & Xianliang Hu. (2020). Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System. Numerical Mathematics: Theory, Methods and Applications. 9 (4). 686-704. doi:10.4208/nmtma.2016.m1229
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