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Finite element convergence for the Darwin model to Maxwell’s equations. (English) Zbl 0887.65121
The Darwin model of approximation to the Maxwell equations is considered. The solutions of elliptic boundary value problems in the Darwin model by finite element methods are analyzed. To this aim approximate variational formulations for the problem are derived, the well-posedness of the formulation is proved, finite element methods for the variational problems are proposed, the finite element convergence is shown, and error estimates are derived. The \(H(\text{curl}; \Omega)\) and \(H(\text{curl,div;} \Omega)\) variational formulations for the Darwin model approximations are derived.
Reviewer: V.Burjan (Praha)

65Z05 Applications to the sciences
35Q60 PDEs in connection with optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A25 Electromagnetic theory, general
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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