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

1 POEMS - Propagation des Ondes : Etude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique
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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [31 references]

https://hal-cea.archives-ouvertes.fr/cea-02893125
Submitted on : Wednesday, July 8, 2020 - 9:20:19 AM
Last modification on : Tuesday, July 28, 2020 - 9:02:11 AM

### File

CiDM20_submission.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : cea-02893125, version 1

### Citation

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

Record views