A finite element analysis of a pseudostress formulation for the Stokes eigenvalue problem

Abstract

In this paper we analyse a finite element approximation of the Stokes eigenvalue problem. We introduce a variational formulation relying only on the pseudostress tensor and propose a discretization by means of the lowest-order Brezzi–Douglas–Marini mixed finite element. However, similar results hold true for other H(div)-conforming elements, like Raviart–Thomas elements. We show that the resulting scheme provides a correct approximation of the spectrum and prove optimal-order error estimates. Finally, we report some numerical tests supporting our theoretical results.