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

In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the convergence rate for the eigenpair approximations of the Stokes eigenvalue problem. It is based on a postprocessing strategy that contains solving an additional Stokes source problem on an augmented finite element space which can be constructed either by refining the mesh or by using the same mesh but increasing the order of mixed finite element space. Numerical examples are given to confirm the theoretical analysis.