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Acceleration of stabilized finite element discretizations for the Stokes eigenvalue problem

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Abstract

The stabilized finite element method based on local projection stabilization is applied to discretize the Stokes eigenvalue problems, then the corresponding stability and convergence properties are given. Furthermore, we use a postprocessing technique to accelerate the convergence rate of the eigenpair approximations. The postprocessing strategy contains solving an additional Stokes source problem in an augmented finite element space which can be constructed either by refining the mesh, or increasing the order of finite element space. Numerical tests are also provided to confirm the theoretical results.

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Authors and Affiliations

  1. LSEC, ICMSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Hehu Xie

  2. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Xiaobo Yin

Authors
  1. Hehu Xie
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  2. Xiaobo Yin
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Correspondence to Hehu Xie or Xiaobo Yin.

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Communicated by: Jinchao Xu

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Xie, H., Yin, X. Acceleration of stabilized finite element discretizations for the Stokes eigenvalue problem. Adv Comput Math 41, 799–812 (2015). https://doi.org/10.1007/s10444-014-9386-8

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  • DOI: https://doi.org/10.1007/s10444-014-9386-8

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