A new 2-D/3-D transport core solver for the time-independent Boltzmann transport equation is presented. This solver, named Fiesta, is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux into spherical harmonics ( P N method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous scalar flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations discretized using Raviart–Thomas finite elements. Encouraging numerical results are presented.