Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Efficient parallel resolution of the simplified transport equations in mixed-dual formulation
Journal of Computational Physics
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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 P"1 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 P"N equations. We prove the well-posedness of the mixed-hybrid discretization method for the P"1 equations in the dual formulation. A similar proof applies to the primal formulation. This approach generalizes similar results formerly obtained by Babuska 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.