estimates are provided in Section 5.

The model problem {#s2}
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Let $\Omega_C\subset \mathbb{R}^3$ be a bounded polyhedral domain with a Lipschitz boundary $\Gamma$. We denote by $\mathbf{n}_\Gamma$ the unit normal vector on $\Gamma$ that points towards $\Omega_e:= \mathbb{R}^3\setminus \overline \Omega_C$. In order to illustrate the impact of the conductor’s topology in our method, we assume that $\Omega_C$ has a toroidal shape. We notice that the eddy current problem is posed in the whole space with asymptotic conditions on the behaviour of the electric and magnetic fields at infinity. Depending on the nature of the eddy current problem being solved and the geometry involved, a discretization method can be obtained for this problem by either applying a pure finite element approach on a truncated domain or by using a combination of boundary (BEM) and finite elements (FEM), see [@AMV; @Hiptmair; @MS03; @AV09]. The FEM-BEM formulation is posed in the conductor but its implementation is more difficult and it leads to more complex algebraic linear systems of equations. The FEM method needs a large computational domain, but it is simpler and it can provide an alternative in many practical situations. It is the option that we will consider in the following. 