Nonlinear discontinuous finite element transport solutions in the thick diffusion limit in Cartesian coordinates

Radiative transfer problems of practical interest often contain regions that are extremely optically thick and highly diffusive. In multidimensional problems, memory and CPU limitations force the use of spatial cells that are themselves very optically thick. The authors therefore wish to study the performance of numerical transport methods in highly diffusive regions with optically thick spatial cells. Moreover, given the recent advances in highly accurate nonlinear spatial discretizations, they wish to include, if not emphasize, these in their analysis. They discuss a diffusion limit analysis of the family of linear and nonlinear discontinuous finite element methods (DFEMs) on grids of arbitrary polyhedra