耦合对流-扩散-反应问题的Darcy-Forchheimer问题的有限元方法

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-07 DOI:10.1051/m2an/2021066

Toni Sayah, G. Semaan, Faouzi Triki

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引用次数: 2

摘要

在本文中，我们考虑了一个依赖于浓度的非线性外力耦合的对流-扩散-反应问题- Darcy-Forchheimer问题。利用伽辽金方法建立了解的存在性，并证明了解的唯一性。介绍并分析了一种基于有限元法的数值方案。然后对每一种数值格式导出最优先验误差估计。通过数值计算验证了离散化的理论精度。

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Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem

In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm the theoretical accuracy of the discretization.

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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.