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Lower and upper bounds of Stokes eigenvalue problem based on stabilized finite element methods

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Abstract

Two stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are given. They are stabilized conforming element and nonconforming element with local Gauss integration. By using the stabilized nonconforming finite element method, the lower bound of the Stokes eigenvalue is obtained; by using the stabilized conforming finite element method, the upper bound of the Stokes eigenvalue is given. Moreover, numerical tests confirm the theoretical results of the presented methods.

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Acknowledgments

The author is grateful to the editor and the anonymous referees for their helpful comments and suggestions on the revision of the manuscript.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Pengzhan Huang

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  1. Pengzhan Huang
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Correspondence to Pengzhan Huang.

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This work was supported by the China Postdoctoral Science Foundation (Grant No. 2013M530438), the NSF of Xinjiang Province (Grant No. 2013211B01) and the Doctoral Foundation of Xinjiang University (Grant No. BS120102).

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Huang, P. Lower and upper bounds of Stokes eigenvalue problem based on stabilized finite element methods. Calcolo 52, 109–121 (2015). https://doi.org/10.1007/s10092-014-0110-3

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