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In this paper, we analyze a mixed form of a time-dependent eddy current problem formulated in terms of the electric field E. We show that this formulation admits a well-posed saddle point structure when the constraints satisfied by the primary unknown in the dielectric material are handled by means of a Lagrange multiplier. We use Nedelec edge elements and standard nodal finite elements to define a semi-discrete Galerkin scheme. Furthermore, we introduce the corresponding backward-Euler fully-discrete formulation and prove error estimates.

An 𝐸-based mixed formulation for a time-dependent eddy current problem