Abstract
AbstractIn 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] ana priorierror analysis of the method applied to an interface problem is presented. The analysis reveals optimal order discretization error bounds in theH1-norm. In this paper we extend this analysis and derive optimalL2-error bounds.
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