Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
ESAIM: Modélisation mathématique et analyse numérique, Volume 39 (2005) no. 6, pp. 1149-1176.

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 k 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.

DOI: 10.1051/m2an:2005049
Classification: 65M12, 65M60, 78-08, 78A40
Keywords: electromagnetics, finite volume methods, discontinuous Galerkin methods, centered fluxes, leap-frog time scheme, $L^2$ stability, unstructured meshes, absorbing boundary condition, convergence, divergence preservation
Fezoui, Loula ; Lanteri, Stéphane ; Lohrengel, Stéphanie 1; Piperno, Serge 

1 Dieudonné Lab., UNSA, UMR CNRS 6621, Parc Valrose, 06108 Nice Cedex 2, France.
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     title = {Convergence and stability of a discontinuous {Galerkin} time-domain method for the {3D} heterogeneous {Maxwell} equations on unstructured meshes},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Fezoui, Loula; Lanteri, Stéphane; Lohrengel, Stéphanie; Piperno, Serge. Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes. ESAIM: Modélisation mathématique et analyse numérique, Volume 39 (2005) no. 6, pp. 1149-1176. doi : 10.1051/m2an:2005049. http://archive.numdam.org/articles/10.1051/m2an:2005049/

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