title: 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.
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.
authors.affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, United Kingdom.
authors.forename: G
authors.initials: G
authors.lastname: MacDonald
authors.affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, United Kingdom.
authors.forename: J A
authors.initials: JA
authors.lastname: Mackenzie
authors.affiliation: Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, United Kingdom.
authors.forename: M
authors.initials: M
authors.lastname: Nolan
authors.affiliation: The Beatson Institute for Cancer Research, Garscube Estate, Switchback Road, Glasgow, G61 1BD, United Kingdom.
authors.forename: R H
authors.initials: RH
authors.lastname: Insall
keywords: ALE methods; Bulk–surface equations; Cell migration; Chemotaxis; Evolving finite elements; Moving mesh methods; Reaction–diffusion