450 2016        IGPM450.pdf
TITLE L2-Estimates for a High Order 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
DOI 10.1515/jnma-2017-0109
PUBLICATION Journal of Numerical Mathematics
2018, volume 24, issue 2, pp. 85 - 99