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

G. MacDonald, J.A. MacKenzie, M. Nolan, R.H. Insall

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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.
Original languageEnglish
Pages (from-to)207–226
Number of pages28
JournalJournal of Computational Physics
Early online date21 Dec 2015
Publication statusPublished - 16 Mar 2016



  • reaction-diffusion
  • bulk-surface equations
  • cell migration
  • chemotaxis
  • evolving finite elements
  • moving mesh methods
  • ALE methods

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