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Superconvergence and a posteriori error estimates for the Stokes eigenvalue problems

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Abstract

In this paper we consider the finite element approximation of the Stokes eigenvalue problems based on projection method, and derive some superconvergence results and the related recovery type a posteriori error estimators. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares strategy. The results are based on some regularity assumptions for the Stokes equations, and are applicable to the finite element approximations of the Stokes eigenvalue problems with general quasi-regular partitions. Numerical results are presented to verify the superconvergence results and the efficiency of the recovery type a posteriori error estimators.

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China under the Grants 11001027, 11171337, 91130021 and 11201464, and the National Basic Research Program under the Grants 2011CB309705, 2010CB731505 and 2012CB821204.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Huipo Liu

  2. LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei Gong

  3. LCP, Institute of Applied Physics and Computational Mathematics, Beijing, 100094, China

    Shuanghu Wang

  4. LSEC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Ningning Yan

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  1. Huipo Liu
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  2. Wei Gong
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  3. Shuanghu Wang
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  4. Ningning Yan
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Correspondence to Huipo Liu.

Additional information

Communicated by Rolf Stenberg.

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Liu, H., Gong, W., Wang, S. et al. Superconvergence and a posteriori error estimates for the Stokes eigenvalue problems. Bit Numer Math 53, 665–687 (2013). https://doi.org/10.1007/s10543-013-0422-8

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  • DOI: https://doi.org/10.1007/s10543-013-0422-8

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