Spectral element discretization of the Maxwell equations

Belgacem, F.; Bernardi, C.

doi:10.1090/S0025-5718-99-01086-8

Spectral element discretization of the Maxwell equations
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by F. Ben Belgacem and C. Bernardi PDF

Math. Comp. 68 (1999), 1497-1520 Request permission

Abstract:

We consider a variational problem which is equivalent to the electromagnetism system with absorbing conditions on a part of the boundary, and we prove that it is well-posed. Next we propose a discretization relying on a finite difference scheme for the time variable and on spectral elements for the space variables, and we derive error estimates between the exact and discrete solutions. Résumé. On considère un problème variationnel équivalent aux équations de l’électromagnétisme avec conditions aux limites absorbantes sur une partie de la frontière, qu’on prouve être bien posé. Puis on propose une discrétisation de ce problème par schéma aux différences finies en temps et éléments spectraux en espace, et on établit des estimations d’erreur entre solutions exacte et approchée.

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