Nonconforming Finite Elements and Multigrid Methods for Maxwell Eigenvalue Problem

Abstract

The Maxwell eigenvalue problem refers to the task of solving the Maxwell equations under specific boundary conditions. In this paper, we primarily discuss nonconforming finite elements and multigrid methods for Maxwell eigenvalue Problem. 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.