A Non-Conforming Generalization of Raviart-Thomas Elements to the Spherical Harmonic Even-Parity Neutron Transport Equation

Abstract : The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or $P_N$) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2-D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements.