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Preprint-No.: <   450   >   Published in: April 2016   PDF-File: IGPM450.pdf
Title:L2-Error Analysis of an Isoparametric Unfitted Finite Element Method for Elliptic Interface Problems
Authors:Christoph Lehrenfeld, Arnold Reusken
Abstract:
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method was introduced which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. This method is based on a parametric mapping which transforms a piecewise planar interface (or surface) reconstruction to a high order approximation. In the paper [C. Lehrenfeld, A. Reusken, Analysis of a High Order Finite Element Method for Elliptic Interface Problems, arXiv 1602.02970, submitted] an a priori error analysis of the method applied to an interface problem is presented. The analysis reveals optimal order discretization error bounds in the H1-norm. In this paper we extend this analysis and derive optimal L2-error bounds.
Keywords:unfitted finite element method, isoparametric finite element method, high order methods, geometry errors, interface problems, Nitsche's method