362 RWTH Publication No: 230371        2013        IGPM362.pdf
TITLE An Eulerian Space-Time Finite Element Method for Diffusion Problems on Evolving Surfaces
AUTHORS Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
ABSTRACT In this paper, we study numerical methods for the solution of partial differential dequations on evolving surfaces. The evolving hypersurface in Rd defines a d-dimensional space-time manifold in the space-time continuum Rd+1. We derive and analyze a variational formulation for a class of diffusion problems on the space-time manifold. For this variational formulation new well-posedness and stability results are derived. The analysis is based on an inf-sup condition and involves some natural, but non-standard, (anisotropic) function spaces. Based on this formulation a discrete in time variational formulation is introduced that is very suitable as a starting point for a discontinuous Galerkin (DG) space-time finite element discretization. This DG space-time method is explained and results of numerical experiments are presented that illustrate its properties.
KEYWORDS evolving surface, space-time finite element, discontinuous Galerkin
DOI 10.1137/130918149
PUBLICATION SIAM journal on numerical analysis
52(3), 1354-1377 (2014)