Finite Element Formulations of Nodal Schemes for Neutron Diffusion and Transport Problems

Several finite element formulations of nodal schemes for neutron diffusion problems are presented: They include nonconforming primal formulations as well as mixed and mixed-hybrid ones, with exact or approximate evaluation of the matrix coefficients. These different formulations are compared to one another and also related to well-known point- and mesh-centered finite difference schemes. Some numerical results are given in one and two dimensions with different schemes. Applications to two-dimensional neutron transport problems are also proposed through the general approach of transverse integration.