Geodesic
Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods
Applications of Mathematics, Tome 54 (2009) no. 1, pp. 1-15.

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In this paper we analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements, $Q_1^{{\rm rot}}$ and $EQ_1^{{\rm rot}}$. Using the technique of eigenvalue error expansion, the technique of integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.
DOI : 10.1007/s10492-009-0001-0
Classification : 35A35, 35P05, 35P15, 35Q30, 35Q35, 65N12, 65N15, 65N25, 65N30, 76D07, 76M10
Keywords: Stokes eigenvalue problem; stream function-vorticity-pressure method; asymptotic expansion; extrapolation; a posteriori error estimates; nonconforming finite element methods; convergence 
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     title = {Approximation and eigenvalue extrapolation of {Stokes} eigenvalue problem by nonconforming finite element methods},
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Jia, Shanghui; Xie, Hehu; Yin, Xiaobo; Gao, Shaoqin. Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods. Applications of Mathematics, Tome 54 (2009) no. 1, pp. 1-15. doi : 10.1007/s10492-009-0001-0. http://geodesic.mathdoc.fr/articles/10.1007/s10492-009-0001-0/

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