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

journal contribution
posted on 2023-06-08, 00:55 authored by R Barreira, C M Elliott, Anotida Madzvamuse
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 G by a triangulated surface Gh consisting of a union of triangles with vertices on G. A finite element space of functions is then defined by taking the continuous functions on Gh 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.

History

Publication status

  • Published

Journal

Journal of Mathematical Biology

ISSN

0303-6812

Publisher

Springer Verlag

Issue

6

Volume

63

Page range

1095-1119

Department affiliated with

  • Mathematics Publications

Notes

My contribution to this article was 40%

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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