We consider the time-harmonic eddy current problem in its electric formulation
where the conductor is a polyhedral domain. By proving the convergence
in energy, we justify in what sense this problem is the limit of a family of Maxwell
transmission problems: Rather than a low frequency limit, this limit has to be understood
in the sense of Bossavit .
We describe the singularities of the solutions.
They are related to edge and corner singularities of certain problems for the scalar
Laplace operator, namely the interior Neumann problem, the exterior Dirichlet problem,
and possibly, an interface problem. These singularities are the limit of
the singularities of the related family of Maxwell problems.