Nonconforming Finite Elements and Multigrid Methods for Maxwell Eigenvalue Problem

In this paper, we demonstrate that the Maxwell eigenvalue problem can be solved by a nonconforming finite element and multigrid method. By using an appropriate operator, the eigenvalue problem can be viewed as a curl-curl problem. We obtain the approximate optimal error estimates on graded mesh. We also prove the convergence of the W-cycle and full multigrid algorithms for the corresponding discrete problem. The performance of these algorithms is illustrated by numerical experiments.