Comptes Rendus
Partial Differential Equations
Two new discrete inequalities of Poincaré–Friedrichs on discontinuous spaces for Maxwell's equations
[Deux nouvèlles inégalités de type Poincaré–Friedrichs sur les espaces discontinus pour les équations de Maxwell]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 29-32.

On présente deux nouvelles inégalités de type Poincaré–Friedrichs sur les espaces discontinus. La preuve des inégalités est basée sur des formules de décomposition orthogonale de L2(Ω)3.

We present two new discrete inequalities of Poincaré–Friedrichs on discontinuous spaces for Maxwell's equations. The proofs of the inequalities are based on some decompositions formulas of L2(Ω)3.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.026

Abdelhamid Zaghdani 1 ; Christian Daveau 1

1 Univeristé Paris-Sud, laboratoire AN-EDP, département de mathématiques, UMR 8628, bâtiment 425, 91405 Orsay cedex, France
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Abdelhamid Zaghdani; Christian Daveau. Two new discrete inequalities of Poincaré–Friedrichs on discontinuous spaces for Maxwell's equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 1, pp. 29-32. doi : 10.1016/j.crma.2005.10.026. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.026/

[1] V. Girault; P.A. Raviart Finite Element Methods for Navier–Stokes Equations, Springer-Verlag, Berlin, 1986

[2] F. Kikuchi Mixed formulations for finite element analysis of magnetostatic and electrostatic problems, Japan J. Appl. Math, Volume 6 (1989), pp. 209-221

[3] J.L. Lions; E. Magenes Problèmes aux limites non homogènes et applications, Dunot, Paris, 1968

[4] S. Prudhomme, F. Pascal, J.T. Oden, A. Romkes, Review of a priori estimation for discontinuous Galerkin method, Tech. report 2000-27, TICAM, University of Texas at Austin, 2000

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