Solution of Multi-Dimensional Neutron Transport Equation by Finite Element Method

Abstract

A scheme of treatment with the finite element Galerkin method is proposed for the approximation of solutions of multidimensional steady state neutron transport equations, and it is proved that the approximate solutions yielded by the treatment converge to the solutions of the transport equations under reasonable hypotheses. These approximate solutions are used also to show the existence of weak solutions of transport equations. Finally, based on the Galerkin method, the conditions for convergence are discussed for the multi-group approximation and for the method of spherical harmonics.