# 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

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topCreusé, 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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