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Superconvergence of the finite element method for the Stokes eigenvalue problem

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  • Sheng, Ying
  • Zhang, Tie
  • Pan, Zixing

Abstract

In this paper we consider the stable P1 – P1 finite element pair solving the Stokes eigenvalue problem and derive some superconvergence results based on the interpolation post-processing technique. Firstly, we derive the superclose property of the interpolation function. Then a superconvergence result of O(h3/2)-order for the pressure approximation and the velocity gradient approximation under the condition of strong regular mesh triangulation are obtained. Finally, the superconvergence rate of O(h3)-order is proved for the eigenvalue approximation and the numerical experiment is provided to confirm the theoretical analysis.

Suggested Citation

  • Sheng, Ying & Zhang, Tie & Pan, Zixing, 2021. "Superconvergence of the finite element method for the Stokes eigenvalue problem," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100059x
    DOI: 10.1016/j.chaos.2021.110706
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    References listed on IDEAS

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    1. Zhifeng Weng & Yaoxiong Cai, 2017. "An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-9, December.
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      Keywords

      P1 - P1 Finite element pair; Superconvergence; A post-processing technique; Stokes eigenvalue problem;
      All these keywords.

      JEL classification:

      • P1 - Political Economy and Comparative Economic Systems - - Capitalist Economies
      • P1 - Political Economy and Comparative Economic Systems - - Capitalist Economies

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