A finite element method for the neutron transport equation in an infinite cylindrical domain

摘要

We study the spatial discretization, in a fully discrete scheme, for the numerical solution of a model problem for the neutron transport equation in an infinite cylindrical domain. Based on using an interpolation technique in the discontinuous Galerkin finite element procedure, we derive an almost optimal error estimate for the scalar flux in the L-2-norm. Combining a duality argument applied to the above result together with the previous semidiscrete error estimates for the velocity discretizations, we also obtain globally optimal error bounds for the critical eigenvalues. [References: 12]