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In this paper, the stabilized finite element method based on local projectionis applied to discretize the Stokes eigenvalue problems and the correspondingconvergence analysis is given. Furthermore, we also use a method to improve theconvergence rate for the eigenpair approximations of the Stokes eigenvalueproblem. It is based on a postprocessing strategy that contains solving anadditional Stokes source problem on an augmented finite element space which canbe constructed either by refining the mesh or by using the same mesh butincreasing the order of mixed finite element space. Numerical examples aregiven to confirm the theoretical analysis.

Postprocessing and Higher Order Convergence of Stabilized Finite Element Discretizations of the Stokes Eigenvalue Problem