  We develop a robust cut finite element method for a model of diffusion in
fractured media consisting of a bulk domain with embedded cracks. The crack has
its own pressure field and can cut through the bulk mesh in a very general
fashion. Starting from a common background bulk mesh, that covers the domain,
finite element spaces are constructed for the interface and bulk subdomains
leading to efficient computations of the coupling terms. The crack pressure
field also uses the bulk mesh for its representation. The interface conditions
are a generalized form of conditions of Robin type previously considered in the
literature which allows the modeling of a range of flow regimes across the
fracture. The method is robust in the following way: 1. Stability of the
formulation in the full range of parameter choices; and 2. Not sensitive to the
location of the interface in the background mesh. We derive an optimal order a
priori error estimate and present illustrating numerical examples.
