A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds : application to a model of cell migration and chemotaxis

MacDonald, G. and MacKenzie, J.A. and Nolan, M. and Insall, R.H. (2016) A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds : application to a model of cell migration and chemotaxis. Journal of Computational Physics, 309. 207–226. ISSN 0021-9991

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    Abstract

    In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.