Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
ESAIM: Modélisation mathématique et analyse numérique, Volume 40 (2006) no. 2, pp. 413-430.

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.

DOI: 10.1051/m2an:2006017
Classification: 65N25, 65N30
Keywords: DG method, Maxwell's system, discrete compactness, eigenvalue approximation
Creusé, Emmanuel ; Nicaise, Serge 1

1 Université de Valenciennes et du Hainaut Cambrésis, MACS, Le Mont Houy, 59313 Valenciennes Cedex 9, France. http://www.univ-valenciennes.fr/macs/Serge.Nicaise
     author = {Creus\'e, Emmanuel and Nicaise, Serge},
     title = {Discrete compactness for a discontinuous {Galerkin} approximation of {Maxwell's} system},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {413--430},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {2},
     year = {2006},
     doi = {10.1051/m2an:2006017},
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Creusé, Emmanuel; Nicaise, Serge. Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system. ESAIM: Modélisation mathématique et analyse numérique, Volume 40 (2006) no. 2, pp. 413-430. doi : 10.1051/m2an:2006017. http://archive.numdam.org/articles/10.1051/m2an:2006017/

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