ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve.
ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve.
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DOI：
10.1016/j.enganabound.2013.10.008
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发表时间：
2014-01
影响因子：
3.3
通讯作者：
Praetorius D
中科院分区：
文献类型：
--
作者：
Feischl M;Führer T;Karkulik M;Praetorius D
在自适应有限元法（FEM）中，Zienkiewicz和Zhu（1987）提出的ZZ-误差估计在数学上已经得到了很好的建立，并在实际中得到了广泛的应用。在这项工作中，我们提出并分析了自适应边界元法（BEM）的ZZ型误差估计。我们考虑弱奇异和超奇异积分方程，并证明，特别是相关的自适应网格细化算法的收敛性。在整个过程中，理论研究结果强调数值实验。
In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) 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.