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

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

1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
2 SERMA - Service d’Études des Réacteurs et de Mathématiques Appliquées

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.

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

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Patrick Ciarlet, Minh Hieu Do, François Madiot. A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations. 2020. ⟨hal-03936904v1⟩