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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.

L 2 -error analysis of an isoparametric unfitted finite element method for elliptic interface problems