Multigrid methods for two-dimensional Maxwell's equations on graded meshes

In this paper we investigate the numerical solution for two-dimensional Maxwell's equations on graded meshes. The approach is based on the Hodge decomposition. The solution u of Maxwell's equations is approximated by solving standard second order elliptic problems. Quasi-optimal error estimates for both u and ×u in the L2 norm are obtained on graded meshes. We prove the uniform convergence of the W-cycle and full multigrid algorithms for the resulting discrete problem. The performance of these methods is illustrated by numerical results.