ALE_3_Styles_ELL_bjourdocOct2012.pdf (7.05 MB)
An ALE ESFEM for solving PDEs on evolving surfaces
journal contribution
posted on 2023-06-08, 08:12 authored by Charles Martin Elliott, Vanessa StylesVanessa StylesNumerical 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.
History
Publication status
- Published
File Version
- Submitted version
Journal
Milan Journal of MathematicsISSN
1424-9286Publisher
Springer VerlagExternal DOI
Issue
2Volume
80Page range
469-501Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes