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

摘要: In the context of unfitted finite element discretizations realization high order methods is challenging due to fact that geometry approximation has be sufficiently accurate. Recently a new method was introduced which achieves for domains are implicitly described by smooth level set functions. This based on parametric mapping transforms piecewise planar interface (or surface) reconstruction approximation. paper [C. Lehrenfeld, A. Reusken, \emph{Analysis High Order Finite Element Method Elliptic Interface Problems}, arXiv 1602.02970, Accepted publication in IMA J. Numer. Anal.] an priori error analysis applied problem presented. The reveals optimal discretization bounds $H^1$-norm. this we extend and derive $L^2$-error bounds.