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Comptes Rendus Mathématique
Volume 334, n° 4
pages 293-298 (2002)
Doi : S1631-073X(02)02221-5
Received : 15 October 2001 ;  accepted : 26 November 2001
Régularité spatio-temporelle de la solution des équations de Maxwell dans des domaines non convexes
Space-time regularity of the solution to Maxwell's equations in non-convex domains
 

Emmanuelle Garcia a , Simon Labrunie b
a CEA/DAMIle-de France, BP 12, 91680 Bruyères-le-Châtel, France 
b Institut Elie Cartan, Université Henri Poincaré, Nancy I, 54506 Vandœuvre-lès-Nancy cedex, France 

Note présentée par Roland Glowinski

Résumé

La méthode du complément singulier, développée afin de résoudre les équations de Maxwell dans des domaines non convexes (cf. [5,2] pour des domaines bidimensionnels en absence et en présence de charges, [3] pour des domaines axisymétriques), est basée sur une décomposition orthogonale de l'espace des solutions. Après avoir rappelé les résultats classiques de régularité dans des domaines lipschitziens, nous donnons plusieurs résultats de régularité en espace et en temps de la solution et de ses composantes, qui sont valables dans plusieurs géométries effectivement utilisées en calcul numérique. Pour citer cet article : E. Garcia, S. Labrunie, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 293-298.

The full text of this article is available in PDF format.
Abstract

The Singular Complement Method, developed in order to solve Maxwell's equations in non-convex domains (cf. [5,2] for two-dimensional domains in absence and in presence of charges, [3] for axisymmetric domains), is based on an orthogonal decomposition of the space of solutions. After recalling the classical regularity results in Lipschitz domains, we give several results of space and time regularity of the solution and of its components, which are valid for several geometries effectively used for numerical computations. To cite this article: E. Garcia, S. Labrunie, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 293-298.

The full text of this article is available in PDF format.


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