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Preprint-No.: <   386   >   Published in: March 2014   PDF-File: IGPM386.pdf
Title:A Space-Time FEM for PDES on Evolving Surfaces
Authors:Jörg Grande, Maxim A. Olshanskii, Arnold Reusken
Abstract:
The paper studies a finite element method for computing transport and diffusion along evolving surfaces. The method does not require a parametrization of a surface or an extension of a PDE from a surface into a bulk outer domain. The surface and its evolution may be given implicitly, e.g., as the solution of a level set equation. This approach naturally allows a surface to undergo topological changes and experience local geometric singularities. The numerical method uses space-time finite elements and is provably second order accurate. The paper reviews the method, error estimates and shows results for computing the diffusion of a surfactant on surfaces of two colliding droplets.
Keywords:evolving surface, diffusion, space-time finite elements, discontinuous Galerkin
Publication:In Proceedings of the 11th World Congress on Computational Mechanics, 2014,
E. Onate, J. Oliver and A. Huerta (Eds).