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L2-error analysis of an isoparametric unfitted finite element method for elliptic interface problems
Journal of Numerical Mathematics ( IF 3 ) Pub Date : 2019-06-26 , DOI: 10.1515/jnma-2017-0109
Christoph Lehrenfeld , Arnold Reusken

Abstract 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 H1-norm. In this paper we extend this analysis and derive optimal L2-error bounds.

中文翻译:

用于椭圆界面问题的等参未拟合有限元方法的 L2 误差分析

摘要 在未拟合的有限元离散化的背景下,由于几何近似必须足够准确,因此高阶方法的实现具有挑战性。最近引入了一种新的未拟合的有限元方法,该方法实现了由平滑水平集函数隐式描述的域的几何形状的高阶近似。该方法基于将分段平面界面(或表面)重建转换为高阶近似的参数映射。在论文 [C. Lehrenfeld 和 A. Reusken,IMA J. Numer。肛门。38 (2018), No. 3, 1351–1387] 提出了应用于接口问题的方法的先验误差分析。该分析揭示了 H1 范数中的最优阶离散化误差界限。
更新日期:2019-06-26
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