On the approximation of the divergence of electromagnetic fields by edge elements

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Résumé : Edge elements are a popular way to approximate electromagnetic fields, for which convergence is obtained in H(curl)-norm. In this talk, we first prove that the divergence of the fields is always well approximated in some weak norm for the time-harmonic problems. Then, for the static problems, we propose a new discretization scheme that also allows to control the error on the divergence of the fields. We show how this scheme compares to the discretization of the usual mixed formulation. Finally, we illustrate those results by some numerical experiments.