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.
Mots-clés : DG method, Maxwell's system, discrete compactness, eigenvalue approximation
@article{M2AN_2006__40_2_413_0,
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},
zbl = {1112.78020},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006017/}
}
TY - JOUR AU - Creusé, Emmanuel AU - Nicaise, Serge TI - Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 413 EP - 430 VL - 40 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006017/ DO - 10.1051/m2an:2006017 LA - en ID - M2AN_2006__40_2_413_0 ER -
%0 Journal Article %A Creusé, Emmanuel %A Nicaise, Serge %T Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 413-430 %V 40 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006017/ %R 10.1051/m2an:2006017 %G en %F M2AN_2006__40_2_413_0
Creusé, Emmanuel; Nicaise, Serge. Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 2, pp. 413-430. doi : 10.1051/m2an:2006017. http://www.numdam.org/articles/10.1051/m2an:2006017/
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