Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part I. The two-dimensional case
Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. Part I. The two-dimensional case
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DOI：
10.1093/imanum/20.2.203
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发表时间：
2000-04-01
影响因子：
2.1
通讯作者：
Faermann, B
中科院分区：
文献类型：
--
作者：
Faermann, B
在本文中，我们表明在二维情况下，Aronszajn-Slobodeckij范数\\。\\（Hs）（（Gamma））（由非整数s是R->0 \ N的元素的二重积分给出）对于特殊函数是可局部化的。基于这一结果，我们引入新的局部后验误差指标的Galerkin离散的边界积分方程。误差指标是有效的和可靠的广泛的一类积分算子，特别是负序算子。既不需要逆估计，也不需要饱和性质的效率或可靠性的证明。误差指标基于可计算残差的局部范数，并且可以用于控制自适应细化。数值算例验证了理论结果。
In this paper we show in the two-dimensional case that the Aronszajn-Slobodeckij norm \\ . \\(Hs) ((Gamma)) (given by a double integral for a non-integer s is an element of R->0 \ N) is localizable for special functions. Based on this result, we introduce new local a posteriori error indicators for the Galerkin discretization of boundary integral equations. The error indicators are efficient and reliable for a wide class of integral operators, in particular for operators of negative order. Neither inverse estimates nor saturation properties are needed for the proof of efficiency or reliability. The error indicators are based on local norms of the computable residual and can be used for controlling the adaptive refinement. Numerical examples confirm the theoretical results.