双孔隙-斯托克斯模型的弱伽勒金有限元法

IF 1.3 4区数学 Q1 MATHEMATICS International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI:10.4208/ijnam2024-1023

Lin Yang,Wei Mu,Hui Peng, Xiuli Wang

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引用次数: 0

摘要

本文介绍了双孔隙-斯托克斯模型的弱 Galerkin 有限元方法。双孔隙-斯托克斯模型通过四个界面条件将双孔隙方程与斯托克斯方程耦合在一起。在该方法中，我们定义了几个弱 Galerkins 有限元空间和弱微分算子。我们为模型提供了弱伽勒金方案，并建立了数值方案的良好拟合性。推导了能量规范误差的最佳收敛阶数。最后，我们验证了在不同网格上使用不同弱 Galerkin 元素的数值方法的有效性。

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The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model

In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with the Stokes equations through four interface conditions. In this method, we define several weak Galerkin finite element spaces and weak differential operators. We provide the weak Galerkin scheme for the model, and establish the well-posedness of the numerical scheme. The optimal convergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of the numerical method with different weak Galerkin elements on different meshes.

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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.