| 450 | 2016 IGPM450.pdf |
| TITLE | L2-Estimates for a High Order Unfitted Finite Element Method for Elliptic Interface Problems |
| AUTHORS | Christoph Lehrenfeld, 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, 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 H1-norm. In this paper we extend this analysis and derive optimal L2-error bounds. |
| KEYWORDS | unfitted finite element method, isoparametric finite element method, high order methods, geometry errors, interface problems, Nitsche's method |
| DOI | 10.1515/jnma-2017-0109 |
| PUBLICATION | Journal of Numerical Mathematics 2018, volume 24, issue 2, pp. 85 - 99 |
