A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2024-06-01 DOI:10.4208/ijnam2024-1018

Kai He,Junjie Chen,Li Zhang, Maohua Ran

引用次数: 0

Abstract

In this paper, we propose a new method for the Darcy-Stokes equations based on the stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the stabilizer term by increasing the degree of polynomial approximation space of the weak gradient operator. Compared with the classical weak Galerkin finite element method, it will not increase the size of global stiffness matrix. We show that the new algorithm not only has a simpler formula, but also reduces the computational complexity. Optimal order error estimates are established for the corresponding numerical approximation in various norms. Finally, we numerically illustrate the accuracy and convergence of this method.

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达西-斯托克斯方程的无稳定器弱 Galerkin 有限元方法

本文提出了一种基于无稳定项弱 Galerkin 有限元法的达西-斯托克斯方程新方法。在所提出的方法中，我们通过增加弱梯度算子多项式近似空间的度数来去除稳定项。与经典的弱 Galerkin 有限元方法相比，它不会增加全局刚度矩阵的大小。我们证明，新算法不仅公式更简单，而且降低了计算复杂度。我们为相应的数值近似建立了各种规范下的最优阶误差估计。最后，我们用数值说明了该方法的准确性和收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.