A virtual element approximation for the pseudostress formulation of the Stokes eigenvalue problem

Abstract

In this paper we analyze a virtual element method (VEM) for a pseudostress formulation of the Stokes eigenvalue problem. This formulation allows to eliminate the velocity and the pressure, leading to an elliptic formulation where the only unknown is the pseudostress tensor. Adapting the non-compact operator theory, we prove that our method provides a correct approximation of the spectrum and is spurious free. We derive optimal a priori error estimates, which we confirm with some numerical tests. Also we present a computational spurious analysis of the proposed method.