Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 309, Issue -, Pages 207-226Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.12.038
Keywords
Reaction-diffusion; Bulk-surface equations; Cell migration; Chemotaxis; Evolving finite elements; ALE methods; Moving mesh methods
Funding
- UK Engineering and Physical Sciences Research Council (EPSRC)
- Cancer Research UK
- Cancer Research UK [15672]
- [RF-2014-522]
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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. (C) 2016 The Authors. Published by Elsevier Inc.
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