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Preprint-No.: <   376   >   Published in: October 2013   PDF-File: IGPM376_k.pdf
Title:Error Analysis of a Space-Time Finite Element Method for Solving PDES on Evolving Surfaces
Authors:Maxim A. Olshanskii, Arnold Reusken
Abstract:
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in Rd , d = 2, 3. The method employs discontinuous piecewise linear in time – continuous piecewise linear in space finite elements and is based on a space-time weak formulation of a surface PDE problem. Trial and test surface finite element spaces consist of traces of standard volumetric elements on a space-time manifold resulting from the evolution of a surface. We prove first order convergence in space and time of the method in an energy norm and second order convergence in a weaker norm. Furthermore, we derive regularity results for solutions of parabolic PDEs on an evolving surface, which we need in a duality argument used in the proof of the second order convergence estimate.
Keywords:evolving surface, space-time finite elements, discontinuous Galerkin
DOI: 10.1137/130936877
Publication:SIAM journal on numerical analysis
52(4), 2092-2120 (2014)