, Volume 80, Issue 2, pp 469501
First online:
An ALE ESFEM for Solving PDEs on Evolving Surfaces
 Charles M. ElliottAffiliated withMathematics Institute, University of Warwick Email author
 , Vanessa StylesAffiliated withDepartment of Mathematics, University of Sussex
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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.
Mathematics Subject Classification (2010)
Primary 65M60 65M15 Secondary 35K99 35R01 35R37 76R99Keywords
Surface finite elements ALE advection diffusion equation interface motion Title
 An ALE ESFEM for Solving PDEs on Evolving Surfaces
 Journal

Milan Journal of Mathematics
Volume 80, Issue 2 , pp 469501
 Cover Date
 201212
 DOI
 10.1007/s0003201201956
 Print ISSN
 14249286
 Online ISSN
 14249294
 Publisher
 SP Birkhäuser Verlag Basel
 Additional Links
 Topics
 Keywords

 Primary 65M60
 65M15
 Secondary 35K99
 35R01
 35R37
 76R99
 Surface finite elements
 ALE
 advection diffusion equation
 interface motion
 Authors

 Charles M. Elliott ^{(1)}
 Vanessa Styles ^{(2)}
 Author Affiliations

 1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
 2. Department of Mathematics, University of Sussex, Brighton, BN1 9QH, UK