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

卷:309

Article

MacDonald, G.¹  Mackenzie, J. A.¹  Nolan, M.¹  Insall, R. H.² 

[1] Univ Strathclyde, Dept Math & Stat, Glasgow G1 1XH, Lanark, Scotland

[2] Beatson Inst Canc Res, Garscube Estate,Switchback Rd, Glasgow G61 1BD, Lanark, Scotland

关键词: Reaction-diffusion;    Bulk-surface equations;    Cell migration;    Chemotaxis;    Evolving finite elements;    ALE methods;    Moving mesh methods;   

DOI  :  10.1016/j.jcp.2015.12.038

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free