Feischl Michael, Führer Thomas, Karkulik Michael, Praetorius Dirk
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.
Eng Anal Bound Elem. 2014 Jan;38(100):49-60. doi: 10.1016/j.enganabound.2013.10.008.
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.
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。
