|| IGPM450.pdf April 2016 |
|| L2-Estimates for a High Order Unfitted Finite Element Method for Elliptic Interface Problems |
||Christoph Lehrenfeld, Arnold Reusken|
||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. |
|| unfitted finite element method, isoparametric finite element method, high order methods, geometry errors, interface problems, Nitsche's method |