{"title":"A Stabilizer-Free Weak Galerkin Finite Element Method for the Darcy-Stokes Equations","authors":"Kai He,Junjie Chen,Li Zhang, Maohua Ran","doi":"10.4208/ijnam2024-1018","DOIUrl":null,"url":null,"abstract":"In this paper, we propose a new method for the Darcy-Stokes equations based on\nthe stabilizer-free weak Galerkin finite element method. In the proposed method, we remove the\nstabilizer term by increasing the degree of polynomial approximation space of the weak gradient\noperator. Compared with the classical weak Galerkin finite element method, it will not increase\nthe size of global stiffness matrix. We show that the new algorithm not only has a simpler formula,\nbut also reduces the computational complexity. Optimal order error estimates are established for\nthe corresponding numerical approximation in various norms. Finally, we numerically illustrate\nthe accuracy and convergence of this method.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Analysis and Modeling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/ijnam2024-1018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
