386 IGPM386.pdf        March 2014
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).