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

Patrick Ciarlet (1) , Minh Hieu Do (2) , François Madiot (2, 3)

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 SERMA - Service d’Études des Réacteurs et de Mathématiques Appliquées
3 LLPR - Laboratoire de Logiciels pour la Physique des Réacteurs

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.

Mots clés: Neutronics; diffusion equation; mixed formulation; low regularity solution; a posteriori error estimates; mesh refinement

Domaines: Mathématiques [math]; Physique [physics]

Patrick Ciarlet, Minh Hieu Do, François Madiot. A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (1), pp.1-27. ⟨10.1051/m2an/2022078⟩. ⟨hal-03936904v2⟩