L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems

Abstract

n 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 and A. Reusken, IMA J. Numer. Anal. 38 (2018), No. 3, 1351–1387] 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.