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Preprint-No.: <   362   >   Published in: April 2013   PDF-File: IGPM362_k.pdf
Title:An Eulerian Space-Time Finite Element Method for Diffusion Problems on Evolving Surfaces
Authors:Maxim A. Olshanskii, Arnold Reusken, Xianmin Xu
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)