Even- and Odd-Parity Finite Element Solutions to Thick Diffusive Problems in Cartesian Geometry

We review the behavior of even- and odd-parity finite element discretizations for thick diffusive transport problems in 3D Cartesian geometry. We show that the linear continuous finite element discretization of the odd-parity equations violates the discrete inf-sup condition on triangular and tetrahedral meshes. We examine the properties of the coupled even- and odd-parity equations discretized with the lowest order Raviart-Thomas elements, which satisfy the inf-sup condition. We conclude with a description of our diffusion synthetic acceleration scheme and present XY-geometry numerical results. (author)