Geodesic
Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
Creusé, Emmanuel  ; Nicaise, Serge1 
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
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 2, pp. 413-430

Voir la notice de l'article provenant de la source Numdam

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 
@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 },
     pages = {413--430},
     publisher = {EDP-Sciences},
     volume = {40},
     number = {2},
     year = {2006},
     doi = {10.1051/m2an:2006017},
     zbl = {1112.78020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
PY  - 2006
SP  - 413
EP  - 430
VL  - 40
IS  - 2
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
%D 2006
%P 413-430
%V 40
%N 2
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 40 (2006) no. 2, pp. 413-430. doi: 10.1051/m2an:2006017

Cité par Sources :