Mixed-hybrid discretization methods for the P1 equations

We consider mixed-hybrid discretization methods for the linear Boltzmann transport equation which is extensively used in computational neutron transport. Mixed-hybrid methods combine attractive features of both mixed and hybrid methods, namely the simultaneous approximation of the flux and current, and the use of Lagrange multipliers to enforce interface regularity constraints.In the present contribution, we cover the case of the P1 equations which represent the simplest approximation to the Boltzmann equation still retaining typical transport features. This constitutes a necessary preliminary step for the study of the general PN equations.We prove the well-posedness of the mixed-hybrid discretization method for the P1 equations in the dual formulation. A similar proof applies to the primal formulation. This approach generalizes similar results formerly obtained by Babuška et al. for the primal formulation of the diffusion equation. Also, it provides a mathematical basis for various discretization techniques commonly used in nuclear reactor analysis.