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

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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 (https://doi.org/10.1016/j.jcp.2015.12.038)

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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.

ORCID iDs

MacDonald, G. ORCID logoORCID: https://orcid.org/0000-0001-6318-3340, MacKenzie, J.A. ORCID logoORCID: https://orcid.org/0000-0003-4412-7057, Nolan, M. ORCID logoORCID: https://orcid.org/0000-0003-0748-2236 and Insall, R.H.;
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