Paper Info
Title
L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems
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 H-1-norm. In this paper we extend this analysis and derive optimal L-2-error bounds.
Year
DOI
Venue
2019
10.1515/jnma-2017-0109
JOURNAL OF NUMERICAL MATHEMATICS
Keywords
DocType
Volume
unfitted finite element method,isoparametric finite element method,high order methods,geometry errors,interface problems,Nitsche's method
Journal
27
Issue
ISSN
Citations 
2
1570-2820
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Christoph Lehrenfeld1467.55
Arnold Reusken230544.91