Analysis of a high order unfitted finite element method for elliptic interface problems

Lehrenfeld C, Reusken A

Research article (journal) | 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. We consider a new unfitted finite element method which achieves a high order approximation of the geometry for domains which are implicitly described by smooth level set functions. The method is based on a parametric mapping which transforms a piecewise planar interface (or surface) reconstruction to a high order approximation. Both components, the piecewise planar interface reconstruction and the parametric mapping are easy to implement. In this paper we present an a priori error analysis of the method applied to an interface problem. The analysis reveals optimal order error bounds for the geometry approximation and for the finite element approximation, for arbitrary high order discretization. The theoretical results are confirmed in numerical experiments.

Details about the publication

Volume1602.02970
Statussubmitted / under review
Release year2016 (10/02/2016)
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)