Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
Creusé, Emmanuel ; Nicaise, Serge
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 40 (2006), p. 413-430 / Harvested from Numdam
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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.

Publié le : 2006-01-01
DOI : https://doi.org/10.1051/m2an:2006017
Classification:  65N25,  65N30 
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     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},
     volume = {40},
     year = {2006},
     pages = {413-430},
     doi = {10.1051/m2an:2006017},
     zbl = {1112.78020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2006__40_2_413_0}
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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, Tome 40 (2006) pp. 413-430. doi : 10.1051/m2an:2006017. http://gdmltest.u-ga.fr/item/M2AN_2006__40_2_413_0/

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