a1 CERMICS, INRIA, BP93, 06902 Sophia-Antipolis Cedex, France. Serge.Piperno@cermics.enpc.fr
a2 Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved for metallic cavities. Convergence is proved for Discontinuous elements on tetrahedral meshes, as well as a discrete divergence preservation property. Promising numerical examples with low-order elements show the potential of the method.
(Received August 17 2004)
(Revised July 2 2005)
(Online publication November 15 2005)
Mathematics Subject Classification: