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Approximation of an Eigenvalue Problem Associated with the Stokes Problem by the Stream Function-Vorticity-Pressure Method

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Abstract

By means of eigenvalue error expansion and integral expansion techniques, we propose and analyze the stream function-vorticity-pressure method for the eigenvalue problem associated with the Stokes equations on the unit square. We obtain an optimal order of convergence for eigenvalues and eigenfuctions. Furthermore, for the bilinear finite element space, we derive asymptotic expansions of the eigenvalue error, an efficient extrapolation and an a posteriori error estimate for the eigenvalue. Finally, numerical experiments are reported.

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Authors and Affiliations

  1. School of Economics, Shandong University, Jinan, 250100, P.R. China

    Wei Chen

  2. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Academia Sinica, Beijing, 100080, P.R. China

    Qun Lin

Authors
  1. Wei Chen
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  2. Qun Lin
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Additional information

The first author was supported by China Postdoctoral Sciences Foundation.

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Chen, W., Lin, Q. Approximation of an Eigenvalue Problem Associated with the Stokes Problem by the Stream Function-Vorticity-Pressure Method. Appl Math 51, 73–88 (2006). https://doi.org/10.1007/s10492-006-0006-x

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  • DOI: https://doi.org/10.1007/s10492-006-0006-x

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