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Spectral element discretization of the Maxwell equations

Author(s): F. Ben Belgacem; C. Bernardi.
Journal: Math. Comp. 68 (1999), 1497-1520.
MSC (1991): Primary 65N35; Secondary 35Q60
Posted: March 1, 1999
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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. RESUME. 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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Additional Information:

F. Ben Belgacem
Affiliation: M.I.P. (UMR C.N.R.S. 5640), Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France
Email: belgacem@mip.ups-tlse.fr

C. Bernardi
Affiliation: Analyse Numérique, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
Email: bernardi@ann.jussieu.fr

DOI: 10.1090/S0025-5718-99-01086-8
PII: S 0025-5718(99)01086-8
Received by editor(s): August 4, 1997
Received by editor(s) in revised form: February 19, 1998
Posted: March 1, 1999
Copyright of article: Copyright 1999, American Mathematical Society

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