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Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Published online by Cambridge University Press:  21 June 2006

Emmanuel Creusé  and
Serge Nicaise
Emmanuel Creusé
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9, France. Emmanuel.Creuse@univ-valenciennes.fr; Serge.Nicaise@univ-valenciennes.fr
Serge Nicaise
Affiliation:
Université de Valenciennes et du Hainaut Cambrésis, MACS, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9, France. Emmanuel.Creuse@univ-valenciennes.fr; Serge.Nicaise@univ-valenciennes.fr
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Abstract

In this paper we prove the discrete compactness property for a discontinuous Galerkin approximation of Maxwell's system on quite general tetrahedral meshes. As a consequence, a discrete Friedrichs inequality is obtained and the convergence of the discrete eigenvalues to the continuous ones is deduced using the theory of collectively compact operators. Some numerical experiments confirm the theoretical predictions.

Keywords

DG methodMaxwell's systemdiscrete compactnesseigenvalue approximation.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 2 , March 2006 , pp. 413 - 430
Copyright
© EDP Sciences, SMAI, 2006

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