Radiative transfer equations have been proven useful models in various applications such as photon propagation in biological tissue. Due to the high-dimensionality of the radiative transfer equation and the anisotropy of the solution the numerical approximation of this equation is challenging. We will present a numerical scheme which allows for efficient assembly and storage of a discrete approximation of the corresponding differential operator. To this end, we introduce an inconsistently perturbed problem, which is based on a modification of the boundary conditions. We present basic estimates for the consistency error and discuss corresponding approximation error estimates as well as memory complexity.