Summary: For the simulation of fractured porous media, a common approach is the use of co-dimension one models for the fracture description. In order to simulate correctly the behavior at fracture crossings, standard models are not sufficient because they either cannot capture all important flow processes or are computationally inefficient. We propose a new concept to simulate co-dimension one fracture crossings and show its necessity and accuracy by means of an example and a comparison to a literature benchmark. From the application point of view, often the pressure is known only at a limited number of discrete points and an interpolation is used to define the boundary condition at the remaining parts of the boundary. The quality of the interpolation, especially in fracture models, influences the global solution significantly. We propose a new method to interpolate boundary conditions on boundaries that are intersected by fractures and show the advantages over standard interpolation methods.