曲线上自适应边界元方法的ZZ型后验误差估计器

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve.

作者信息

Feischl Michael, Führer Thomas, Karkulik Michael, Praetorius Dirk

机构信息

Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstr. 8-10/E101/4, 1040 Wien, Austria.

Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile.

出版信息

Eng Anal Bound Elem. 2014 Jan;38(100):49-60. doi: 10.1016/j.enganabound.2013.10.008.

DOI:10.1016/j.enganabound.2013.10.008

PMID:24748725

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC3990432/

Abstract

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments.

摘要

在自适应有限元方法（FEM）的背景下，以齐恩凯维奇和朱（1987）[52]命名的ZZ误差估计器在数学上已得到充分确立，并在实践中广泛使用。在这项工作中，我们提出并分析了用于自适应边界元方法（BEM）的ZZ型误差估计器。我们考虑弱奇异和超奇异积分方程，并特别证明了相关自适应网格细化算法的收敛性。在整个过程中，数值实验突出了理论结果。