Chen, Wei; Lin, Qun Approximation of an eigenvalue problem associated with the Stokes problem by the stream function-vorticity-pressure method. (English) Zbl 1164.65489 Appl. Math., Praha 51, No. 1, 73-88 (2006). Summary: 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. Cited in 38 Documents 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 76D07 Stokes and related (Oseen, etc.) flows 76M10 Finite element methods applied to problems in fluid mechanics 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 Keywords:eigenvalue problem; Stokes problem; stream function-vorticity-pressure method; error expansion; convergence; eigenfunctions; bilinear finite element; extrapolation; error estimate; numerical experiments × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link References: [1] I. Babuska, J. Osborn: Eigenvalue problems. Handbook of Numerical Analysis, Vol. II, Finite Element Method (Part I) (P. G. Ciarlet, J. L. 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