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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2009

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

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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Dates and versions

hal-00291503 , version 1 (27-06-2008)
hal-00291503 , version 2 (02-07-2008)

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Cite

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, 2009, 19 (11), pp.1959-1994. ⟨10.1142/S0218202509004017⟩. ⟨hal-00291503v2⟩
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