A type of multi-level correction scheme for eigenvalue problems by nonconforming finite element methods

In this paper, a type of multi-level correction scheme is proposed to solve eigenvalue problems by nonconforming finite element methods. With this new scheme, the accuracy of eigenpair approximations can be improved after each correction step which only needs to solve a source problem on finer finite element space and an eigenvalue problem on a coarse finite element space. This correction scheme can improve the efficiency of solving eigenvalue problems by the nonconforming finite element method. Furthermore, the same as the direct eigenvalue solving by the nonconforming finite element method, this multi-level correction method can also produce the lower-bound approximations of the eigenvalues.