The surface finite element method for pattern formation on evolving biological surfaces

Barreira, R, Elliott, C M and Madzvamuse, A (2011) The surface finite element method for pattern formation on evolving biological surfaces. Journal of Mathematical Biology, 63 (6). pp. 1095-1119. ISSN 0303-6812

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Abstract

In this article we propose models and a numerical method for pattern formation on evolving curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the material transport formula, surface gradients and diffusive conservation laws. The evolution of the surface is defined by a material surface velocity. The numerical method is based on the evolving surface finite element method. The key idea is based on the approximation of Γ by a triangulated surface Γh consisting of a union of triangles with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. To demonstrate the capability, flexibility, versatility and generality of our methodology we present results for uniform isotropic growth as well as anisotropic growth of the evolution surfaces and growth coupled to the solution of the reaction-diffusion system. The surface finite element method provides a robust numerical method for solving partial differential systems on continuously evolving domains and surfaces with numerous applications in developmental biology, tumour growth and cell movement and deformation.

Item Type: Article
Additional Information: My contribution to this article was 40%
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Anotida Madzvamuse
Date Deposited: 06 Feb 2012 20:00
Last Modified: 03 Jul 2012 08:30
URI: http://sro.sussex.ac.uk/id/eprint/23521
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