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

• Autores: Jintao Cui
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 255, Nº 1, 2014, págs. 231-247
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.05.007
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• Resumen

  • 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.