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, Tome 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 ${ℙ}_{k}$ 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
Mots clés : 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},
pages = {1149--1176},
publisher = {EDP-Sciences},
volume = {39},
number = {6},
year = {2005},
doi = {10.1051/m2an:2005049},
zbl = {1094.78008},
mrnumber = {2195908},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2005049/}
}
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, Tome 39 (2005) no. 6, pp. 1149-1176. doi : 10.1051/m2an:2005049. http://www.numdam.org/articles/10.1051/m2an:2005049/

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