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

Emmanuel Creusé (1, 2) , Serge Nicaise (3)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SIMPAF - SImulations and Modeling for PArticles and Fluids
3 LAMAV - Laboratoire de Mathématiques et leurs Applications de Valenciennes - EA 4015

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.

Mots clés: DG method; Maxwell’s system; discrete compactness; eigenvalue approximation

Domaines: Analyse numérique [math.NA]

Emmanuel Creusé, Serge Nicaise. Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system. ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (2), pp.413-430. ⟨10.1051/m2an:2006017⟩. ⟨hal-00768645⟩