Numerical analysis of the generalized Maxwell equations (with an elliptic correction) for charged particle simulations

Patrick Ciarlet 1 Simon Labrunie 2, 3
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
3 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : When computing numerical solutions to the Vlasov--Maxwell equations, the source terms in Maxwell's equations usually fail to satisfy the continuity equation. Since this condition is required for the well-posedness of Maxwell's equations, it is necessary to introduce generalized Maxwell's equations which remain well-posed when there are errors in the sources. These approaches, which involve a hyperbolic, a parabolic and an elliptic correction, have been recently analyzed mathematically. The goal of this paper is to carry out the numerical analysis for several variants of Maxwell's equations with an elliptic correction.
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Patrick Ciarlet, Simon Labrunie. Numerical analysis of the generalized Maxwell equations (with an elliptic correction) for charged particle simulations. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2009, 19 (11), pp.1959-1994. ⟨10.1142/S0218202509004017⟩. ⟨hal-00291503v2⟩

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