Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries

Patrick Ciarlet 1 Erell Jamelot 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : A few years ago, Costabel and Dauge proposed a variational setting, which allows one to solve numerically the time-harmonic Maxwell equations in 3D geometries with the help of a continuous approximation of the electromagnetic field. In this paper, we investigate how their framework can be adapted to compute the solution to the time-dependent Maxwell equations. In addition, we propose some extensions, such as the introduction of a mixed variational setting and its discretization, to handle the constraint on the divergence of the field. © 2007 Elsevier Inc. All rights reserved.
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Patrick Ciarlet, Erell Jamelot. Continuous Galerkin methods for solving the time-dependent Maxwell equations in 3D geometries. Journal of Computational Physics, Elsevier, 2007, 226 (1), pp.1122-1135. ⟨10.1016/j.jcp.2007.05.029⟩. ⟨hal-00876227⟩

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