Discrete compactness for a discontinuous Galerkin approximation of Maxwell's system
Emmanuel Creusé, Serge Nicaise · ESAIM Mathematical Modelling and Numerical Analysis · 2006
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.