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Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods

Shanghui Jia; Hehu Xie; Xiaobo Yin; Shaoqin Gao — 2009

Applications of Mathematics

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, $Q_{1}^{rot}$ and $E Q_{1}^{rot}$ . 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.

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