A Lumped Linear-Discontinuous Spatial Discretization Scheme for Triangular-Mesh S_n Calculations in r-z Geometry

A lumped linear-discontinuous spatial finite element discretization of the S_n equations in r-z geometry on triangular meshes is derived and computationally tested. An asymptotic analysis indicates that the scheme preserves the thick diffusion limit and behaves well with unresolved boundary layers. Computational results are presented that indicate the scheme is second-order accurate in the transport regime and that confirm the main predictions of the asymptotic diffusion-limit analysis.