A Continuous Finite Element-Based, Discontinuous Finite Element Method for S_N Transport

A class of discontinuous finite element methods (DFEMs) is proposed for spatially discretizing the S_N transport equation in multidimensions. Mesh cells are first subdivided into simplexes. Equations for the angular fluxes in a cell are then generated by computing the linear DFEM S_N equations for a simplex on each subelement and assembling the equations over the subelements. The result is a (piecewise) linear continuous finite element method spatial discretization on the cell that is coupled discontinuously to its neighbors through the standard DFEM upwinding technique. The method is presented in two-dimensional Cartesian coordinates. Numerical experiments indicate the method has numerical properties that are suitable for a new S_N spatial discretization.