Mixed Methods for the Velocity-Pressure-Pseudostress Formulation of the Stokes Eigenvalue Problem

In two and three dimensions, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The consist schemes: velocity pressure are approximated with piecewise polynomial, whereas pseudostress consider classic families elements ${H}(\div)$ spaces: Raviart--Thomas Brezzi--Douglas--Marini elements. With aid spectral theory compact operators, prove that our method does not introduce spurious modes. Also, obtain convergence error estimates proposed methods. We report numerical results to compare accuracy robustness between both schemes.