Milan Journal of Mathematics

, Volume 80, Issue 2, pp 469–501

An ALE ESFEM for Solving PDEs on Evolving Surfaces

Article

DOI: 10.1007/s00032-012-0195-6

Cite this article as:
Elliott, C.M. & Styles, V. Milan J. Math. (2012) 80: 469. doi:10.1007/s00032-012-0195-6

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.

Mathematics Subject Classification (2010)

Primary 65M6065M15Secondary 35K9935R0135R3776R99

Keywords

Surface finite elementsALEadvection diffusion equationinterface motion

Copyright information

© Springer Basel 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of MathematicsUniversity of SussexBrightonUK