The reduced basis method is by now a well established tool for solving parameter dependent problems. While it is well understood for elliptic equations, parametric convection-dominated problems still pose severe difficulties: On the one hand, one has to guarantee an inf-sup stability of the reduced bases. On the other hand, these problems do not come with natural norms rendering them well-conditioned which is problematic for residual based error estimators and the greedy construction of the reduced bases.
After giving a short overview of the reduced basis method, a well-conditioned variational formulation and a corresponding stabilization scheme for the radiative transfer problem are presented. Since this scheme naturally overcomes the above problems, it is then used as a starting point for a reduced basis method for the radiative transfer problem.