Extrapolation and superconvergence of the Steklov eigenvalue problem

被引：0
|
作者：
Mingxia Li
Qun Lin
Shuhua Zhang
机构：
[1] Chinese Academy of Sciences,Academy of Mathematics and Systems Science
[2] Tianjin University of Finance and Economics,Research Center for Mathematics and Economics
来源：
Advances in Computational Mathematics | 2010年 / 33卷
关键词：
The Steklov eigenvalue problem; Graded meshes; Richardson extrapolation; Superconvergence; A posteriori error estimators; 76S05; 45K05; 65M12; 65M60; 65R20;
D O I：
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中图分类号：
学科分类号：
摘要：
On the basis of a transform lemma, an asymptotic expansion of the bilinear finite element is derived over graded meshes for the Steklov eigenvalue problem, such that the Richardson extrapolation can be applied to increase the accuracy of the approximation, from which the approximation of O(h3.5) is obtained. In addition, by means of the Rayleigh quotient acceleration technique and an interpolation postprocessing method, the superconvergence of the bilinear finite element is presented over graded meshes for the Steklov eigenvalue problem, and the approximation of O(h3) is gained. Finally, numerical experiments are provided to demonstrate the theoretical results.
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页码：25 / 44
页数：19
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