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Improved Mixed and Hybrid Discretization of the Transport Equation in Slab Geometry

In this article we deal with a mixed and hybrid finite element method slab geometry discretization of the transport equation arising from the new variational formulation introduced in Cartier and Peybernes (2011). The aim of this study is to construct such a discretization by preserving the diffusion limit in the entire diffusive region, close to the boundaries, and for internal interface problems.