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Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method. (English) Zbl 1340.65258
Summary: This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of J. Li et al. [Numer. Methods Partial Differ. Equations 28, No. 1, 115–126 (2012; Zbl 1234.65038)], which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.

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