Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system

Emmanuel Creusé; Serge Nicaise

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 2, page 413-430
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Creusé, Emmanuel, and Nicaise, Serge. "Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system." ESAIM: Mathematical Modelling and Numerical Analysis 40.2 (2006): 413-430. <http://eudml.org/doc/249688>.

@article{Creusé2006,
abstract = { 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. },
author = {Creusé, Emmanuel, Nicaise, Serge},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {DG method; Maxwell's system; discrete compactness; eigenvalue approximation.; Galerkin approximation; eigenvalue approximation},
language = {eng},
month = {6},
number = {2},
pages = {413-430},
publisher = {EDP Sciences},
title = {Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system},
url = {http://eudml.org/doc/249688},
volume = {40},
year = {2006},
}

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
DA - 2006/6//
PB - EDP Sciences
VL - 40
IS - 2
SP - 413
EP - 430
AB - 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.
LA - eng
KW - DG method; Maxwell's system; discrete compactness; eigenvalue approximation.; Galerkin approximation; eigenvalue approximation
UR - http://eudml.org/doc/249688
ER -

References

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