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Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods

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Abstract

In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, Q rot1 and EQ rot1 . Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.

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Authors and Affiliations

  1. School of Applied Mathematics, Central University of Finance and Economics, Beijing, 100081, P.R.China

    Shanghui Jia

  2. LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, P.R.China

    Hehu Xie & Xiaobo Yin

  3. College of Mathematics and Computer, Hebei University, Baoding, 071002, P.R.China

    Shaoqin Gao

Authors
  1. Shanghui Jia
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  2. Hehu Xie
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  3. Xiaobo Yin
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  4. Shaoqin Gao
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Corresponding author

Correspondence to Shanghui Jia.

Additional information

This project is supported in part by the National Natural Science Foundation of China (10471103) and is subsidized by the National Basic Research Program of China under the grant 2005CB321701.

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Jia, S., Xie, H., Yin, X. et al. Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods. Appl Math 54, 1–15 (2009). https://doi.org/10.1007/s10492-009-0001-0

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  • DOI: https://doi.org/10.1007/s10492-009-0001-0

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