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Moving Finite Element Simulations for Reaction-Diffusion Systems

Moving Finite Element Simulations for Reaction-Diffusion Systems
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Year:    2012

Author:    Guanghui Hu, Zhonghua Qiao, Tao Tang

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 3 : pp. 365–381

Abstract

This work is concerned with the numerical simulations for two reaction-diffusion systems, i.e., the Brusselator model and the Gray-Scott model. The numerical algorithm is based upon a moving finite element method which helps to resolve large solution gradients. High quality meshes are obtained for both the spot replication and the moving wave along boundaries by using proper monitor functions. Unlike [33], this work finds out the importance of the boundary grid redistribution which is particularly important for a class of problems for the Brusselator model. Several ways for verifying the quality of the numerical solutions are also proposed, which may be of important use for comparisons.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.10-m11180

Advances in Applied Mathematics and Mechanics, Vol. 4 (2012), Iss. 3 : pp. 365–381

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Reaction-diffusion systems Brusselator model Gray-Scott model moving finite element method.

Author Details

Guanghui Hu

Zhonghua Qiao

Tao Tang

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