A weak Galerkin finite element method for the Navier-Stokes equations

被引：39
作者：
Liu, Xin [1 ]
Li, Jian [2 ,3 ]
Chen, Zhangxin [1 ,4 ]
机构：
[1] Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China
[2] Shaanxi Univ Sci & Technol, Sch Arts & Sci, Xian 710021, Shaanxi, Peoples R China
[3] Baoji Univ Arts & Sci, Dept Math, Baoji 721007, Peoples R China
[4] Univ Calgary, Schulich Sch Engn, Dept Chem & Petr Engn, 2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2018年 / 333卷
关键词：
Weak Galerkin; Finite element methods; Navier-Stokes equations; More general partitions; 2ND-ORDER ELLIPTIC PROBLEMS; BIHARMONIC EQUATION; HELMHOLTZ-EQUATION; POLYTOPAL MESHES; FLOW;
D O I：
10.1016/j.cam.2017.11.010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose and analyze a weak Galerkin finite element method for the Navier-Stokes equations. The new formulation hinges upon the introduction of weak gradient, weak divergence and weak trilinear operators. Moreover, by choosing the matching finite element triples, this new method not only obtains stability and optimal error estimates but also has a lot of attractive computational features: general finite element partitions of arbitrary polygons or polyhedra with certain shape regularity and parameter free. Finally, several numerical experiments assess the convergence properties of the new method and show its computational advantages. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：442 / 457
页数：16
相关论文
共 35 条
[1]  
[Anonymous], 1986, SPRINGER SERIES COMP
[2]  
[Anonymous], 1984, THEORY NUMERICAL ANA
[3]   Unified analysis of discontinuous Galerkin methods for elliptic problems [J].
Arnold, DN ;
Brezzi, F ;
Cockburn, B ;
Marini, LD .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2002, 39 (05) :1749-1779
[4]  
Benzi M, 2005, ACTA NUMER, V14, P1, DOI 10.1017/S0962492904000212
[5]  
BRENNER S. C., 2008, MATH THEORY FINITE E, VThird
[6]  
Brezzi F., 1991, Mixed and Hybrid Finite Element Methods, V15
[7]   Weak Galerkin method for the coupled Darcy-Stokes flow [J].
Chen, Wenbin ;
Wang, Fang ;
Wang, Yanqiu .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2016, 36 (02) :897-921
[8]  
Chen Z., 2005, Finite Element Methods and Their Applications
[9]  
Ciarlet P., 2002, Classics in Appl. Math., V40
[10]  
CROUZEIX M, 1989, MATH COMPUT, V52, P437, DOI 10.1090/S0025-5718-1989-0958870-8
1234