Implications of Mesh Structure to Solutions of Reaction-Diffusion Systems on Fixed and Growing DomainsReaction-diffusion systems have been widely used in developmental biology and most of these systems comprise of nonlinear reaction terms which makes it difficult to find closed form solutions. It therefore becomes convenient to look for numerical solutions: finite difference, finite elements, finite volume and spectral methods are typical examples of the numerical methods used.
In this talk, we present the implications of mesh structure to solutions of reacting and diffusing systems on fixed and growing domains. We illustrate computationally that the finite difference scheme imposes symmetry to solutions if regular mesh elements are used on regular domains. Such solutions are not observed if, for example, asymmetric mesh or randomly chosen mesh elements are used. We compare our results to those obtained by use of the finite and moving grid finite element method on unstructured triangular elements.
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