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Licensed Unlicensed Requires Authentication Published by De Gruyter January 30, 2018

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

  • Christoph Lehrenfeld EMAIL logo and 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 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.

Classification: 65N30; 65N15; 65D05
  1. Funding: C. Lehrenfeld gratefully acknowledges funding by the German Science Foundation (DFG) within the project LE 3726/1-1.

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Received: 2017-08-31
Revised: 2017-12-15
Accepted: 2017-12-17
Published Online: 2018-01-30
Published in Print: 2019-06-26

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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