A boundary functional for the least-squares finite-element solution of neutron transport problems

The least-squares finite-element framework for the neutron transport equati on is based on the minimization of a least-squares functional applied to th e properly scaled neutron transport equation. This approach is extended by incorporating the boundary conditions into the least-squares functional. Th e proof of the V-ellipticity and continuity of the new functional leads to bounds of the discretization error for different regimes. For a P-1 approxi mation of the angular dependence the resulting system of partial differenti al equations for the moments is explicitly derived. In the diffusion limit this system is essentially a Poisson equation for the zeroth moment and has a divergence structure for the set of moments of order 1. One of the key f eatures of the least-squares approach is that it produces a posteriori erro r bounds. The use of these bounds is demonstrated in numerical examples for a spatial discretization using trilinear finite elements on a uniform tess ellation into cubes.