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Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods. (English) Zbl 1212.65434
Summary: We analyze the stream function-vorticity-pressure method for the Stokes eigenvalue problem. Further, we obtain a full order convergence rate of the eigenvalue approximations for the Stokes eigenvalue problem based on asymptotic error expansions for two nonconforming finite elements \(Q_1^{\mathrm {rot}}\) and \(EQ_1^{\mathrm {rot}}\). Using the eigenvalue error expansion, integral identities and the extrapolation method, we can improve the accuracy of the eigenvalue approximations.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35Q30 Navier-Stokes equations
35P15 Estimates of eigenvalues in context of PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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