In this paper we propose and analyze a virtual element method for the two dimensional non-symmetric diffusion-convection eigenvalue problem in order to derive a priori and a posteriori error estimates. Under the classic assumptions of the meshes, and with the aid of the classic theory of compact operators, we prove error estimates for the eigenvalues and eigenfunctions. Also, we develop an a posteriori error estimator which, in one hand, results to be reliable and on the other, with standard bubble functions arguments, also results to be efficient. We test our method on domains where the complex eigenfunctions are not sufficiently regular, in order to assess the performance of the estimator that we compare with the uniform refinement given by the a priori analysis

翻译：本文提出并分析了一种针对二维非对称扩散-对流特征值问题的虚拟元方法，旨在推导先验和后验误差估计。在网格的标准假设下，借助紧算子经典理论，我们证明了特征值和特征函数的误差估计。此外，我们开发了一个后验误差估计子，一方面该估计子是可靠的，另一方面通过标准泡函数论证，它也是有效的。我们通过在复杂特征函数正则性不足的区域上测试该方法，以评估该估计子的性能，并将其与先验分析给出的均匀细化结果进行比较。