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Two-level stabilized finite element method for Stokes eigenvalue problem

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Abstract

A two-level stabilized finite element method for the Stokes eigenvalue problem based on the local Gauss integration is considered. This method involves solving a Stokes eigenvalue problem on a coarse mesh with mesh size H and a Stokes problem on a fine mesh with mesh size h = O(H 2), which can still maintain the asymptotically optimal accuracy. It provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution, which involves solving a Stokes eigenvalue problem on a fine mesh with mesh size h. Hence, the two-level stabilized finite element method can save a large amount of computational time. Moreover, numerical tests confirm the theoretical results of the present method.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P. R. China

    Peng-zhan Huang  (黄鹏展), Yin-nian He  (何银年) & Xin-long Feng  (冯新龙)

  2. Center for Computational Geoscienes, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, P. R. China

    Yin-nian He  (何银年)

Authors
  1. Peng-zhan Huang  (黄鹏展)
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  2. Yin-nian He  (何银年)
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  3. Xin-long Feng  (冯新龙)
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Corresponding author

Correspondence to Yin-nian He  (何银年).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10901131, 10971166, and 10961024), the National High Technology Research and Development Program of China (No. 2009AA01A135), and the Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2010211B04)

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Huang, Pz., He, Yn. & Feng, Xl. Two-level stabilized finite element method for Stokes eigenvalue problem. Appl. Math. Mech.-Engl. Ed. 33, 621–630 (2012). https://doi.org/10.1007/s10483-012-1575-7

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  • DOI: https://doi.org/10.1007/s10483-012-1575-7

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