The finite volume method based on stabilized finite element for the stationary Navier-Stokes problem

被引：15
|
作者：
He, Guoliang [1 ]
He, Yinnian [1 ]
机构：
[1] Xi An Jiao Tong Univ, Fac Sci, State Key Lab Multiphase Flow Power Engn, Xian 710049, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 205卷 / 01期
关键词：
stationary Navier-Stokes equations; finite volume method; stabilized finite element; error estimation;
D O I：
10.1016/j.cam.2006.07.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A finite volume method based on stabilized finite element for the two-dimensional stationary Navier-Stokes equations is investigated in this work. A macroelement condition is introduced for constructing the local stabilized formulation for the problem. We obtain the well-posedness of the FVM based on stabilized finite element for the stationary Navier-Stokes equations. Moreover, for quadrilateral and triangular partition, the optimal H-1 error estimate of the finite volume solution mu(h) and L-2 error estimate for p(h) are introduced. Finally, we provide a numerical example to confirm the efficiency of the FVM. (C) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码：651 / 665
页数：15
相关论文
共 50 条
  • [1] Stabilized finite element method for the non-stationary Navier-Stokes problem
    He, YN
    Lin, YP
    Sun, WW
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2006, 6 (01): : 41 - 68
  • [2] A stabilized finite volume method for the stationary Navier-Stokes equations
    Sheng, Ying
    Zhang, Tie
    Jiang, Zhong-Zhong
    [J]. CHAOS SOLITONS & FRACTALS, 2016, 89 : 363 - 372
  • [3] Multiscale enrichment of a finite volume element method for the stationary Navier-Stokes problem
    Wen, Juan
    He, Yinnian
    Yang, Jianhong
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2013, 90 (09) : 1938 - 1957
  • [4] Finite volume method based on stabilized finite elements for the nonstationary Navier-Stokes problem
    He, Guoliang
    He, Yinnian
    Feng, Xinlong
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2007, 23 (05) : 1167 - 1191
  • [5] A parallel stabilized finite element method for the Navier-Stokes problem
    Han, Jing
    Du, Guangzhi
    Mi, Shilin
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 170 : 33 - 41
  • [6] Stabilized finite-element method for the stationary Navier-Stokes equations
    Yinnian He
    Aiwen Wang
    Liquan Mei
    [J]. Journal of Engineering Mathematics, 2005, 51 : 367 - 380
  • [7] Stabilized finite-element method for the stationary Navier-Stokes equations
    He, YN
    Wang, AW
    Mei, LQ
    [J]. JOURNAL OF ENGINEERING MATHEMATICS, 2005, 51 (04) : 367 - 380
  • [8] Stabilized multiscale finite element method for the stationary Navier-Stokes equations
    Ge, Zhihao
    Feng, Minfu
    He, Yinnian
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 354 (02) : 708 - 717
  • [9] RECOVERY-BASED ERROR ESTIMATOR FOR STABILIZED FINITE ELEMENT METHOD FOR THE STATIONARY NAVIER-STOKES PROBLEM
    Song, Lina
    Su, Haiyan
    Feng, Xinlong
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2016, 38 (06): : A3758 - A3772
  • [10] Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem
    Wen, Juan
    He, Yinnian
    Zhao, Xin
    [J]. INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2016, 26 (08) : 2462 - 2485
12345