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A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations

Patrick Ciarlet 1 Minh-Hieu Do 2 François Madiot 2
1 POEMS - Propagation des Ondes : Etude Mathématique et Simulation
Inria Saclay - Ile de France, CNRS - Centre National de la Recherche Scientifique, UMA - Unité de Mathématiques Appliquées
Abstract : We analyse $a\ posteriori$ error estimates for the discretization of the neutron diffusion equations with mixed finite elements. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion equation. We pay particular attention to AMR strategies on Cartesian meshes, since such structures are common for nuclear reactor core applications. We exhibit a robust marker strategy for this specific constraint, the $direction\ marker$ strategy. The approach is further extended to a Domain Decomposition Method, the so-called DD+$L^2$ jumps method, as well as to the multigroup neutron diffusion equation.
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https://hal-cea.archives-ouvertes.fr/cea-02893125
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Submitted on : Wednesday, July 8, 2020 - 9:20:19 AM
Last modification on : Saturday, October 10, 2020 - 3:34:32 AM

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Patrick Ciarlet, Minh-Hieu Do, François Madiot. A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations. 2020. ⟨cea-02893125⟩

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