MacDonald, G., Mackenzie, J.A., 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, pp. 207-226. (doi: 10.1016/j.jcp.2015.12.038) (PMID:27330221) (PMCID:PMC4896117)
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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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Insall, Professor Robert |
| Authors: | MacDonald, G., Mackenzie, J.A., Nolan, M., and Insall, R.H. |
| College/School: | College of Medical Veterinary and Life Sciences > School of Cancer Sciences |
| Journal Name: | Journal of Computational Physics |
| Publisher: | Elsevier |
| ISSN: | 0021-9991 |
| ISSN (Online): | 1090-2716 |
| Copyright Holders: | Copyright © 2016 The Authors |
| First Published: | First published in Journal of Computational Physics 309:207-226 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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