A Conforming virtual element approximation for the Oseen eigenvalue problem

Abstract

In this paper we analyze a conforming virtual element method to approximate the eigenfunctions and eigenvalues of the two dimensional Oseen eigenvalue problem. We consider the classic velocity-pressure formulation which allows us to consider the divergence-conforming virtual element spaces employed for the Stokes equations. Under standard assumptions on the meshes we derive a priori error estimates for the proposed method with the aid of the compact operators theory. We report some numerical tests to confirm the theoretical results.