Abstract
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(h 3.5) 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(h 3) is gained. Finally, numerical experiments are provided to demonstrate the theoretical results.
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Communicated by Yuesheng Xu.
This project was supported in part by the National Basic Research Program of China (2007CB814906), the National Natural Science Foundation of China (10471103 and 10771158), Social Science Foundation of the Ministry of Education of China (06JA630047), Tianjin Natural Science Foundation (07JCYBJC14300), and Tianjin University of Finance and Economics.
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Li, M., Lin, Q. & Zhang, S. Extrapolation and superconvergence of the Steklov eigenvalue problem. Adv Comput Math 33, 25–44 (2010). https://doi.org/10.1007/s10444-009-9118-7
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DOI: https://doi.org/10.1007/s10444-009-9118-7
Keywords
- The Steklov eigenvalue problem
- Graded meshes
- Richardson extrapolation
- Superconvergence
- A posteriori error estimators