  We present an error analysis for the discontinuous Galerkin method applied to
the discrete-ordinate discretization of the steady-state radiative transfer
equation. Under some mild assumptions, we show that the DG method converges
uniformly with respect to a scaling parameter $\varepsilon$ which characterizes
the strength of scattering in the system. However, the rate is not optimal and
can be polluted by the presence of boundary layers. In one-dimensional slab
geometries, we demonstrate optimal convergence when boundary layers are not
present and analyze a simple strategy for balance interior and boundary layer
errors. Some numerical tests are also provided in this reduced setting.
