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In this paper we propose and analyze a virtual element method for the twodimensional non-symmetric diffusion-convection eigenvalue problem in order toderive a priori and a posteriori error estimates. Under the classic assumptionsof the meshes, and with the aid of the classic theory of compact operators, weprove error estimates for the eigenvalues and eigenfunctions. Also, we developan a posteriori error estimator which, in one hand, results to be reliable andon the other, with standard bubble functions arguments, also results to beefficient. We test our method on domains where the complex eigenfunctions arenot sufficiently regular, in order to assess the performance of the estimatorthat we compare with the uniform refinement given by the a priori analysis

A priori and a posteriori error analysis for a VEM discretization of the convection-diffusion eigenvalue problem