A Multilevel Correction Method For Convection-diffusion Eigenvalue Problems

In this paper, we propose a multilevel correction method for the convection-diffusion eigenvalue problems, and the method is a new type and efficiency to solve the eigenvalue problems, which is suitable for not only simple but also multiple eigenvalues. In this method, solving eigenvalue problem is transformed to a series of solutions of boundary value problem by the multilevel method on the finest meshes and a serious of eigenvalue problems on the coarsest finite element space. we prove that the accuracy of resulting eigenpair approximations can be improved after each correction step, and in this paper,we give the theoretical proof of this scheme that almost can achieve the optimal accuracy as same as solving the corresponding boundary value problem. Our scheme is easy to realize with Matlab, and numerical results are satisfactory.