  We analyze a numerical method for the coupled system of the eddy current
equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a
bounded domain. The unbounded domain is discretized by means of
finite-element/boundary-element coupling. Even though the considered problem is
strongly nonlinear, the numerical approach is constructed such that only two
linear systems per time step have to be solved. We prove unconditional weak
convergence (of a subsequence) of the finite-element solutions towards a weak
solution. We establish a priori error estimates if a sufficiently smooth strong
solution exists. Numerical experiments underlining the theoretical results are
presented.
