达西-福克海默问题与对流-扩散-反作用方程的后验误差估计

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2024-01-01 DOI:10.4208/ijnam2024-1003

Faouzi Triki,Toni Sayah, Georges Semaan

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引用次数: 0

摘要

在这项研究中，我们推导出了对流-扩散-反应方程与达西-福克海默问题的后验误差估计值，该方程由一个取决于流体浓度的非线性外部源耦合而成。我们引入了与该问题相关的变分公式，并使用有限元法对其进行离散化处理。我们用两类可计算的误差指标证明了最优后验误差。第一种与线性化相关，第二种与离散化相关。然后，我们在精确解的附加规则性假设下找到误差上界和下界。最后，我们进行了数值计算，以显示所获误差指标的有效性。

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A Posteriori Error Estimates for Darcy-Forchheimer’s Problem Coupled with the Convection-Diffusion-Reaction Equation

In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the variational formulation associated to the problem, and discretize it by using the finite element method. We prove optimal a posteriori errors with two types of calculable error indicators. The first one is linked to the linearization and the second one to the discretization. Then we find upper and lower error bounds under additional regularity assumptions on the exact solutions. Finally, numerical computations are performed to show the effectiveness of the obtained error indicators.

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来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.