  We present a coupling of the Finite Element and the Boundary Element Method
in an isogeometric framework to approximate either two-dimensional Laplace
interface problems or boundary value problems consisting in two disjoint
domains. We consider the Finite Element Method in the bounded domains to
simulate possibly non-linear materials. The Boundary Element Method is applied
in unbounded or thin domains where the material behavior is linear. The
isogeometric framework allows to combine different design and analysis tools:
first, we consider the same type of NURBS parameterizations for an exact
geometry representation and second, we use the numerical analysis for the
Galerkin approximation. Moreover, it facilitates to perform h- and
p-refinements. For the sake of analysis, we consider the framework of strongly
monotone and Lipschitz continuous operators to ensure well-posedness of the
coupled system. Furthermore, we provide an a priori error estimate. We
additionally show an improved convergence behavior for the errors in
functionals of the solution that may double the rate under certain assumptions.
Numerical examples conclude the work which illustrate the theoretical results.
