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Ciarlet, Patrick jun.

Augmented formulations for solving Maxwell equations. (English) Zbl 1063.78018

Comput. Methods Appl. Mech. Eng. 194, No. 2-5, 559-586 (2005).
Summary: We consider augmented variational formulations for solving the static or time-harmonic Maxwell equations. For that, a term is added to the usual H (curl) conforming formulations. It consists of a (weighted) \(L^2\) scalar product between the divergence of the EM and the divergence of test fields. In this respect, the methods we present are H (curl, div) conforming. We also build mixed, augmented variational formulations, with either one or two Lagrange multipliers, to dualize the equation on the divergence and, when applicable, the relation on the tangential or normal trace of the field. It is proven that one can derive formulations, which are equivalent to the original static or time-harmonic Maxwell equations. In the latter case, spurious modes are automatically excluded. Numerical analysis and experiments will be presented in the forthcoming paper [the author and E. Jamelot, Augmented formulations for solving Maxwell equations: numerical analysis and experiments, in preparation].

Cited in 34 Documents

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
35Q60 PDEs in connection with optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

Maxwell equations; Augmented variational formulations; Lagrange multipliers
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\textit{P. Ciarlet jun.}, Comput. Methods Appl. Mech. Eng. 194, No. 2--5, 559--586 (2005; Zbl 1063.78018)
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References:

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