Energy norm based a posteriori error estimation for boundary element methods in two dimensions
Energy norm based a posteriori error estimation for boundary element methods in two dimensions
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DOI：
10.1016/j.apnum.2008.12.024
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发表时间：
2009-11-01
影响因子：
2.8
通讯作者：
Praetorius, D.
中科院分区：
文献类型：
--
作者：
Erath, C.;Ferraz-Leite, S.;Praetorius, D.
后验误差估计是可靠、高效的Galerkin边界元计算的重要工具。我们分析了IS的h-h/2-误差估计之间的数学关系。Ferraz-Leite，D.Praetorius，h-型边界元方法的简单后验误差估计器，计算83(2008)135-162]，IS的两级误差估计器。Funken，Schnelle Losungsverfahren for FEM-BEM Koppengsgleichungen，博士论文，汉诺威大学，1996(德文)；R Mund，E.Stephan，J.Weisse，两层方法在R-3中，计算60(1998)243-266]，以及[C.Carstensen，D.Praetorius，有效数值解Symm第一类积分方程的平均技术，SIAM J.Sci].电脑。27(2006)1226-1260]。我们本质上证明了所有这些都是等价的，并且我们扩展了IS的分析。首页--期刊主要分类--期刊细介绍--期刊题录与文摘--期刊详细文摘内容。汉诺威大学博士论文，1996(德文)；P.Mund，E.Stephan，J.Weisse，R-3中单层势的两级方法，计算60(1998)243-266]以涵盖自适应网格加密。因此，所有误差估计器都给出了Galerkin误差的下界，而上界主要取决于饱和假设。作为模型例子，我们考虑了具有弱奇异积分核的二维第一类积分方程解。(C)2009年iMac。爱思唯尔出版，版权所有。
A posteriori error estimation is an important tool for reliable and efficient Galerkin boundary element computations. We analyze the mathematical relation between the h-h/2-error estimator from IS. Ferraz-Leite, D. Praetorius, Simple a posteriori error estimators for the h-version of the boundary element method, Computing 83 (2008) 135-162], the two-level error estimator from IS. Funken, Schnelle Losungsverfahren for FEM-BEM Kopplungsgleichungen, Ph.D. thesis, University of Hannover, 1996 (in German); R Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R-3, Computing 60 (1998) 243-266], and the averaging error estimator from [C. Carstensen, D. Praetorius, Averaging techniques for the effective numerical solution of Symm's integral equation of the first kind, SIAM J. Sci. Comput. 27 (2006) 1226-1260]. We essentially show that all of these are equivalent, and we extend the analysis of IS. Funken, Schnelle Losungsverfahren fur FEM-BEM Kopplungsgleichungen. Ph.D. thesis, University of Hannover, 1996 (in German); P. Mund, E. Stephan, J. Weisse, Two-level methods for the single layer potential in R-3, Computing 60 (1998) 243-266] to cover adaptive mesh-refinement. Therefore, all error estimators give lower bounds for the Galerkin error, whereas upper bounds depend crucially on the saturation assumption. As model examples, we consider first-kind integral equations in 2D with weakly singular integral kernel. (C) 2009 IMACS. Published by Elsevier B.V. All rights reserved.