In the context of unfitted finite element discretizations the realization ofhigh order methods is challenging due to the fact that the geometryapproximation has to be sufficiently accurate. We consider a new unfittedfinite element method which achieves a high order approximation of the geometryfor domains which are implicitly described by smooth level set functions. Themethod is based on a parametric mapping which transforms a piecewise planarinterface (or surface) reconstruction to a high order approximation. Bothcomponents, the piecewise planar interface reconstruction and the parametricmapping are easy to implement. In this paper we present an a priori erroranalysis of the method applied to an interface problem. The analysis revealsoptimal order error bounds for the geometry approximation and for the finiteelement approximation, for arbitrary high order discretization. The theoreticalresults are confirmed in numerical experiments.
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