Convergence of a discontinuous Galerkin scheme for the neutron transport.

Journal article, 2001

We study the spatial discretization 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, and regularizing properties of the solution operator, we derive an {\sl optimal} error estimate in $L_2-$norm for the scalar flux. This result, combined with a duality argument and previously known semidiscrete error estimates for the velocity discretizations, gives {\sl globally optimal} error bounds for the critical eigenvalue.