Abstract
This work is concerned with the numerical simulations for two reactiondiffusion 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.
Original language | English |
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Pages (from-to) | 365-381 |
Number of pages | 17 |
Journal | Advances in Applied Mathematics and Mechanics |
Volume | 4 |
Issue number | 3 |
DOIs | |
Publication status | Published - 25 Oct 2012 |
Keywords
- Brusselator model
- Gray-Scott model
- Moving finite element method
- Reaction-diffusion systems
ASJC Scopus subject areas
- Applied Mathematics
- Mechanical Engineering