Even- and odd-parity finite-element transport solutions in the thick diffusion limit

We analyze the behavior of odd-parity continuous finite-element methods (CFEMs) for problems that contain diffusive regions. We find that each of these method produces a solution that, to leading order inside diffusive regions, satisfies a discretization of the diffusion equation. We find further that these leading-order solutions satisfy boundary conditions that can lead to large errors in the interior solution. We recognize, however, that we can combine an odd-purity CFEM solution and an even-parity CFEM solution and obtain a solution that satisfies very accurate boundary conditions. Our analysis holds in three-dimensional Cartesian geometry, with an arbitrary spatial grid. We give numerical results from slab-geometry; these invariably agree with the predictions of the analysis. Finally, we introduce a rapidly-convergent diffusion-synthetic acceleration scheme for the odd-parity CFEMs, which we believe is new. 18 refs., 3 figs