Volume 4, Issue 3
Moving Finite Element Simulations for Reaction-Diffusion Systems

Guanghui Hu, Zhonghua Qiao & Tao Tang

Adv. Appl. Math. Mech., 4 (2012), pp. 365-381.

Published online: 2012-04

Preview Full PDF 104 1739
Export citation
  • 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.

  • Keywords

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

  • AMS Subject Headings

65M50 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-4-365, author = {Guanghui Hu, Zhonghua Qiao and Tao Tang}, title = {Moving Finite Element Simulations for Reaction-Diffusion Systems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {3}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11180}, url = {http://global-sci.org/intro/article_detail/aamm/125.html} }
TY - JOUR T1 - Moving Finite Element Simulations for Reaction-Diffusion Systems AU - Guanghui Hu, Zhonghua Qiao & Tao Tang JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 365 EP - 381 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11180 UR - https://global-sci.org/intro/article_detail/aamm/125.html KW - Reaction-diffusion systems KW - Brusselator model KW - Gray-Scott model KW - moving finite element method AB -

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.

Guanghui Hu, Zhonghua Qiao & Tao Tang. (1970). Moving Finite Element Simulations for Reaction-Diffusion Systems. Advances in Applied Mathematics and Mechanics. 4 (3). 365-381. doi:10.4208/aamm.10-m11180
Copy to clipboard
The citation has been copied to your clipboard