The convection-diffusion eigenvalue problems are hot topics, and computational mathematics community and physics community are concerned about them in recent years. In this paper, we consider the a posteriori error analysis and the adaptive algorithm of the Crouzeix-Raviart nonconforming element method for the convection-diffusion eigenvalue problems. We give the corresponding a posteriori error estimators, and prove their reliability and efficiency. Finally, the numerical results validate the theoretical analysis and show that the algorithm presented in this paper is efficient.

convection-diffusion eigenvalue problems, the Crouzeix-Raviart element, a posteriori error analysis, adaptive algorithm.