Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
Université de Valenciennes et du Hainaut Cambrésis,
Institut des Sciences et Techniques de Valenciennes,
59313 Valenciennes Cedex 9, France.
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.
Mathematics Subject Classification: 65N25 / 65N30
Key words: DG method / Maxwell's system / discrete compactness / eigenvalue approximation.
© EDP Sciences, SMAI, 2006