460 IGPM460.pdf        November 2016
TITLE Trace Finite Element Methods for PDEs on Surfaces
AUTHORS Maxim A. Olshanskii, Arnold Reusken
ABSTRACT 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