An ALE ESFEM for solving PDEs on evolving surfaces

Elliott, Charles Martin and Styles, Vanessa (2012) An ALE ESFEM for solving PDEs on evolving surfaces. Milan Journal of Mathematics, 80 (2). pp. 469-501. ISSN 1424-9286

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Abstract

Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces
are presented. In the ALE ESFEM the vertices of the triangles evolve with a velocity which is normal to the hypersurface whilst having a tangential velocity which is arbitrary. This is in contrast to the original evolving surface finite element method in which the nodes move with a material velocity. Numerical experiments are presented which illustrate the value of choosing the arbitrary tangential velocity to improve mesh quality. Simulations of two applications arising in material science and biology are presented which couple the evolution of the surface to the solution of the surface partial differential equation.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QH Natural history > QH0301 Biology > QH0426 Genetics > QH0438.4 Special aspects of the subject as a whole, A-Z > QH0438.4.M33 Mathematics
Depositing User: Vanessa Styles
Date Deposited: 08 May 2013 09:11
Last Modified: 14 Mar 2017 00:22
URI: http://sro.sussex.ac.uk/id/eprint/28661

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