On discontinuous Galerkin and discrete ordinates approximations for neutron transport equation and the critical eigenvalue.

The objective of this paper is to give a mathematical framework for a fully discrete numerical approach for the study of the neutron transport equation in a cylindrical domain (container model,). More specifically, we consider the discontinuous Galerkin (DG) finite element method for spatial approximation of the mono-energetic, critical neutron transport equation in an infinite cylindrical domain ωin R3 with a polygonal convex cross-section ω The velocity discretization relies on a special quadrature rule developed to give optimal estimates in discrete ordinate parameters compatible with the quasi-uniform spatial mesh. We use interpolation spaces and derive optimal error estimates, up to maximal available regularity, for the fully discrete scalar flux. Finally we employ a duality argument and prove superconvergence estimates for the critical eigenvalue.