Volume 57, Number 1, January-February 2023
|Page(s)||1 - 27|
|Published online||12 January 2023|
A posteriori error estimates for mixed finite element discretizations of the Neutron Diffusion equations
POEMS, CNRS, INRIA, ENSTA Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France
2 Université Paris-Saclay, CEA, Service d’Études des Réacteurs et de Mathématiques Appliquées, 91191 Gif-sur-Yvette, France
* Corresponding author: email@example.com
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.
Mathematics Subject Classification: 65J10 / 65N15 / 65N30 / 65N50
Key words: Neutronics / diffusion equation / mixed formulation / low regularity solution / a posteriori error estimates / mesh refinement
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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