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Preprint-No.: <   460   >   Published in: November 2016   PDF-File: IGPM460.pdf
Title:Trace Finite Element Methods for PDEs on Surfaces
Authors:Maxim A. Olshanskii, Arnold Reusken
In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of background surface-independent finite element functions are used to approximate the solution of a PDE on a surface. We treat equations on steady and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in detail. We review the error analysis and algebraic properties of the method. The paper navigates through the known variants of the TraceFEM and the literature on the subject.
Keywords:Trace finite elements, PDEs on surfaces, unfitted finite elements