  We consider an interface problem often arising in transport problems: a
coupled system of partial differential equations with one (elliptic) transport
equation on a bounded domain and one equation (in this case the Laplace
problem) on the complement, an unbounded domain. Based on the non-symmetric
coupling of the finite volume method and boundary element method of [Erath et
al., arXiv:1509.00440, 2015] we introduce a robust residual error estimator.
The upper bound of the error in an energy (semi)norm is robust against
variation of the model data. The lower bound, however, additionally depends on
the Peclet number. In several examples we use the local contributions of the
a~posteriori error estimator to steer an adaptive mesh-refining algorithm. The
adaptive FVM-BEM coupling turns out to be an efficient method especially to
solve problems from fluid mechanics, mainly because of the local flux
conservation and the stable approximation of convection dominated problems.
