Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 2, p. 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 : https://doi.org/10.1051/m2an:2006017
Classification:  65N25,  65N30
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {40},
number = {2},
year = {2006},
pages = {413-430},
doi = {10.1051/m2an:2006017},
zbl = {1112.78020},
language = {en},
url = {http://www.numdam.org/item/M2AN_2006__40_2_413_0}
}

Creusé, Emmanuel; Nicaise, Serge. Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 40 (2006) no. 2, pp. 413-430. doi : 10.1051/m2an:2006017. http://www.numdam.org/item/M2AN_2006__40_2_413_0/

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