The Classical Galerkin Finite Element Method Applied to Neutron Diffusion Theory

This chapter aims to present a numerical strategy to solve the neutron diffusion equation (NDE) using the classical finite element method, also known as the Galerkin finite element method (GFEM). To this end, a particular case of the NDE in steady-state and two-dimensional geometry is presented. The mathematical development of the variational formulation of the NDE, when discretized by the GFEM, is then shown. A brief description of the GFEM implementation and a GFEM flowchart for the NDE considering two energy groups are provided. Two benchmark problems are solved using bilinear shape functions for triangular elements and quadrilateral elements. The results corroborate the good convergence rate of the GFEM when compared to the finite difference method (FDM).