Moving Finite Element Simulations for Reaction-Diffusion Systems (Advances in Applied Mathematics and Mechanics, 2012)
This work is concerned with the numerical simulations for two reaction-diffusionsystems, i.e., the Brusselator model and the Gray-Scott model. The numericalalgorithm is based upon a moving finite element method which helps toresolve large solution gradients. High quality meshes are obtained for both thespot replication and the moving wave along boundaries by using proper monitorfunctions. Unlike [33], this work finds out the importance of the boundary gridredistribution which is particularly important for a class of problems for the Brusselatormodel. Several ways for verifying the quality of the numerical solutions arealso proposed, which may be of important use for comparisons.