Lower and Upper Bounds for Stokes Eigenvalues

In this paper, we study the lower and upper bounds for Stokes eigenvalues by finite element schemes. For the schemes studied here, roughly speaking, the loss of the local approximation property of the discrete velocity and pressure spaces may lead to different computed bounds of the eigenvalues. Formally theoretical analysis is constructed based on certain mathematical hypotheses, and numerical experiments are given to illustrate the validity of the theory.