  We consider the numerical approximation of the radiative transfer equation
using discontinuous angular and continuous spatial approximations for the even
parts of the solution. The even-parity equations are solved using a diffusion
synthetic accelerated source iteration. We provide a convergence analysis for
the infinite-dimensional iteration as well as for its discretized counterpart.
The diffusion correction is computed by a subspace correction, which leads to a
convergence behavior that is robust with respect to the discretization. The
proven theoretical contraction rate deteriorates for scattering dominated
problems. We show numerically that the preconditioned iteration is in practice
robust in the diffusion limit. Moreover, computations for the lattice problem
indicate that the presented discretization does not suffer from the ray effect.
The theoretical methodology is presented for plane-parallel geometries with
isotropic scattering, but the approach and proofs generalize to
multi-dimensional problems and more general scattering operators verbatim.
