Resumen de Multigrid methods for two-dimensional Maxwell�s equations on graded meshes

Jintao Cui

• In this paper we investigate the numerical solution for two-dimensional Maxwell�fs equations on graded meshes. The approach is based on the Hodge decomposition. The solution u of Maxwell�fs equations is approximated by solving standard second order elliptic problems.

  Quasi-optimal error estimates for both u and �Þ �~ u in the L2 norm are obtained on graded meshes. We prove the uniform convergence of theW-cycle and full multigrid algorithms for the resulting discrete problem. The performance of these methods is illustrated by numerical results.