  This paper is devoted to study the Arnold-Winther mixed finite element method
for two dimensional Stokes eigenvalue problems using the stress-velocity
formulation. A priori error estimates for the eigenvalue and eigenfunction
errors are presented. To improve the approximation for both eigenvalues and
eigenfunctions, we propose a local post-processing. With the help of the local
post-processing, we derive a reliable a posteriori error estimator which is
shown to be empirically efficient. We confirm numerically the proven higher
order convergence of the post-processed eigenvalues for convex domains with
smooth eigenfunctions. On adaptively refined meshes we obtain numerically
optimal higher orders of convergence of the post-processed eigenvalues even on
nonconvex domains.
