Extrapolation and superconvergence of the Steklov eigenvalue problem
Extrapolation and superconvergence of the Steklov eigenvalue problem
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DOI：
10.1007/s10444-009-9118-7
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发表时间：
2010-07
影响因子：
1.7
通讯作者：
Mingxia Li;Q. Lin;Shuhua Zhang
中科院分区：
文献类型：
--
作者：
Mingxia Li;Q. Lin;Shuhua Zhang
基于一个变换引理，导出了Steklov特征值问题的双线性有限元在梯度网格上的渐近展开式，从而可以应用Richardson外推法来提高逼近精度，并由此得到O（h3.5）的逼近.此外，利用Rayleigh商加速技术和插值后处理方法，证明了Steklov特征值问题双线性有限元在梯度网格上的超收敛性，并得到了O（h3）的逼近.最后，数值实验验证了理论结果。
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 ofO(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 ofO(h3) is gained. Finally, numerical experiments are provided to demonstrate the theoretical results.