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