Energy dependent radiative transfer equation and energy discretization

The radiative transfer equation (RTE) arises in a wide variety of applications. In certain situations, the energy dependence is not negligible. In a series of two papers, we study the energy dependent RTE. In this first paper of the series, we focus on the well-posedness analysis and energy discretization. We use a mixed formulation so that the analysis covers both cases of non-vanishing absorption and vanishing absorption. We introduce a natural energy discretization scheme and derive an optimal order error estimate for the scheme. Angular discretization, spatial discretization and fully discrete schemes, as well as numerical simulation results, are the topics of the sequel.