A priori error analysis of discrete-ordinate weak Galerkin method for radiative transfer equation

This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting semi-discrete hyperbolic system is approximated using the weak Galerkin method. The stability result for the proposed numerical method is devised. A \emph{priori} error analysis is established under the suitable norm. In order to examine the theoretical results, numerical experiments are carried out.