Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

Finite Element Simulations with Adaptively Moving Mesh for the Reaction Diffusion System

Year:    2016

Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2016.m1229

Numerical Mathematics: Theory, Methods and Applications, Vol. 9 (2016), Iss. 4 : pp. 686–704

Published online:    2016-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:   

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