中子扩散方程混合有限元离散化的后验误差估计

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2022-09-20 DOI:10.1051/m2an/2022078

P. Ciarlet, Minh Hieu Do, F. Madiot

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引用次数: 0

摘要

摘要本文分析了混合有限元中子扩散方程离散化的后验误差估计。我们对基块方程，即单群中子扩散方程，给出了保证的局部有效估计。我们特别关注笛卡尔网格上的AMR策略，因为这种结构在核反应堆堆芯应用中很常见。我们展示了一种针对这种特定约束的稳健标记策略，即方向标记策略。

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

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.

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来源期刊

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.