  We derive and analyze a symmetric interior penalty discontinuous Galerkin
scheme for the approximation of the second-order form of the radiative transfer
equation in slab geometry. Using appropriate trace lemmas, the analysis can be
carried out as for more standard elliptic problems. Supporting examples show
the accuracy and stability of the method also numerically, for different
polynomial degrees. For discretization, we employ quad-tree grids, which allow
for local refinement in phase-space, and we show exemplary that adaptive
methods can efficiently approximate discontinuous solutions. We investigate the
behavior of hierarchical error estimators and error estimators based on local
averaging.
