2016/04/15 by Christoph Lehrenfeld, Lehrenfeld, Christoph, Arnold Reusken +1
Computer Science · Engineering · #65D05 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1604.04529
openalex publication_date 2016/04/15 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In the context of unfitted finite element discretizations the realization of\nhigh order methods is challenging due to the fact that the geometry\napproximation has to be sufficiently accurate. Recently a new unfitted finite\nelement method was introduced which achieves a high order approximation of the\ngeometry for domains which are implicitly described by smooth level set\nfunctions. This method is based on a parametric mapping which transforms a\npiecewise planar interface (or surface) reconstruction to a high order\napproximation. In the paper [C. Lehrenfeld, A. Reusken, \Analysis of a\nHigh Order Finite Element Method for Elliptic Interface Problems, arXiv\n1602.02970, Accepted for publication in IMA J. Numer. Anal.] an a priori error\nanalysis of the method applied to an interface problem is presented. The\nanalysis reveals optimal order discretization error bounds in the H1-norm.\nIn this paper we extend this analysis and derive optimal L2-error bounds.\n