BDM H(div) weak Galerkin finite element methods for Stokes equations

被引：4

作者：

Zhang, Shangyou ^{[1
]}

Zhu, Peng ^{[2
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

[2] Jiaxing Univ, Coll Data Sci, Jiaxing 314001, Zhejiang, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2024年 / 197卷

基金：

中国国家自然科学基金;

关键词：

Weak Galerkin methods; H(div) conforming finite element; Stokes equations; Triangular meshes; Tetrahedral meshes; PRESSURE-ROBUST; STABILIZER-FREE; COMPLEXES; OPERATOR; FAMILY; SCHEME;

D O I：

10.1016/j.apnum.2023.11.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We add new inter-element variables to the BDM H(div) finite elements on triangular and tetrahedral meshes for the Stokes equations. With the weak gradient, we enforce weakly the tangential continuity of H(div) finite element velocity fields while not relaxing the normal continuity. The new method produces divergence-free H(div) finite element solutions of optimal order convergence. Numerical examples are provided, confirming the theory and in particular, the pressure-robustness of the method.

引用

页码：307 / 321

页数：15

共 52 条

[1] Arnold D. N., 1992, ADV COMPUTER METHODS
[2] Boffi D., 2013, Mixed Finite Element Methods and Applications, DOI DOI 10.1007/978-3-642-36519-5
[3] Brenner S., 2008, Texts in Applied Mathematics, V3rd ed
[4] ROBUST GLOBALLY DIVERGENCE-FREE WEAK GALERKIN METHODS FOR STOKES EQUATIONS
Chen, Gang
Feng, Minfu
Xie, Xiaoping
[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS, 2016, 34 (05) : 549 - 572
[5] CROUZEIX M, 1973, REV FR AUTOMAT INFOR, V7, P33
[6] DiPietro DA, 2012, MATH APPL-BERLIN, V69, P1, DOI 10.1007/978-3-642-22980-0
[7] Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits
Fabien, Maurice
Guzman, Johnny
Neilan, Michael
Zytoon, Ahmed
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 390
[8] STOKES COMPLEXES AND THE CONSTRUCTION OF STABLE FINITE ELEMENTS WITH POINTWISE MASS CONSERVATION
Falk, Richard S.
Neilan, Michael
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (02) : 1308 - 1326
[9] A Stabilizer-Free Weak Galerkin Finite Element Method for the Stokes Equations
Feng, Yue
Liu, Yujie
Wang, Ruishu
Zhang, Shangyou
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2022, 14 (01) : 181 - 201
[10] Girault V., 1986, FINITE ELEMENT METHO

← 1 2 3 4 5 6 →