Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 6, p. 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 : https://doi.org/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
@article{M2AN_2005__39_6_1149_0,
     author = {Fezoui, Loula and Lanteri, St\'ephane and Lohrengel, St\'ephanie and Piperno, Serge},
     title = {Convergence and stability of a discontinuous Galerkin time-domain method for the 3D heterogeneous Maxwell equations on unstructured meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {6},
     year = {2005},
     pages = {1149-1176},
     doi = {10.1051/m2an:2005049},
     zbl = {1094.78008},
     mrnumber = {2195908},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2005__39_6_1149_0}
}
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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 6, pp. 1149-1176. doi : 10.1051/m2an:2005049. http://www.numdam.org/item/M2AN_2005__39_6_1149_0/

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