L2-estimates for a high order unfitted finite element method for elliptic interface problems

Lehrenfeld C, Reusken A

Working paper | Peer reviewed

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 H^1-norm. In this paper we extend this analysis and derive optimal L^2-error bounds.

Details about the publication

Edition1604.04529
Statussubmitted / under review
Release year2016 (15/04/2016)
Language in which the publication is writtenEnglish
Keywordsunfitted finite element method; isoparametric finite element method; high order methods; geometry errors; interface problems; Nitsche's method

Authors from the University of Münster

Lehrenfeld, Christoph
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)