  We consider a Johnson-N\'ed\'elec FEM-BEM coupling, which is a direct and
non-symmetric coupling of finite and boundary element methods, in order to
solve interface problems for the magnetostatic Maxwell's equations with the
magnetic vector potential ansatz. In the FEM-domain, equations may be
non-linear, whereas they are exclusively linear in the BEM-part to guarantee
the existence of a fundamental solution. First, the weak problem is formulated
in quotient spaces to avoid resolving to a saddle point problem. Second, we
establish in this setting well-posedness of the arising problem using the
framework of Lipschitz and strongly monotone operators as well as a stability
result for a special type of non-linearity, which is typically considered in
magnetostatic applications. Then, the discretization is performed in the
isogeometric context, i.e., the same type of basis functions that are used for
geometry design are considered as ansatz functions for the discrete setting. In
particular, NURBS are employed for geometry considerations, and B-Splines,
which can be understood as a special type of NURBS, for analysis purposes. In
this context, we derive a priori estimates w.r.t. h-refinement, and point out
to an interesting behavior of BEM, which consists in an amelioration of the
convergence rates, when a functional of the solution is evaluated in the
exterior BEM-domain. This improvement may lead to a doubling of the convergence
rate under certain assumptions. Finally, we end the paper with a numerical
example to illustrate the theoretical results, along with a conclusion and an
outlook.
