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.References
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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
- Received by editor(s): August 4, 1997
- Received by editor(s) in revised form: February 19, 1998
- Published electronically: March 1, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Math. Comp. 68 (1999), 1497-1520
- MSC (1991): Primary 65N35; Secondary 35Q60
- DOI: https://doi.org/10.1090/S0025-5718-99-01086-8
- MathSciNet review: 1648355