The divergence-free nonconforming virtual element method for the Navier-Stokes problem

被引：14
作者：
Zhang, Bei [1 ]
Zhao, Jikun [2 ]
Li, Meng [2 ]
机构：
[1] Henan Univ Technol, Sch Sci, Zhengzhou, Peoples R China
[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
来源：
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2023年 / 39卷 / 03期
基金：
中国国家自然科学基金;
关键词：
divergence-free; Navier-Stokes problem; nonconforming virtual element; polygonal mesh; FORMULATION; DARCY;
D O I：
10.1002/num.22812
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present the divergence-free nonconforming virtual element method for the Navier-Stokes problem. By using a gradient projection operator, we construct a nonconforming virtual element that allows us to compute the L-2-projection. The nonconforming virtual element provides the exact divergence-free approximation to the velocity and is proved to be convergent with the optimal convergence rate. Finally, the numerical results are shown to confirm the convergence of the nonconforming virtual element.
引用
收藏
页码：1977 / 1995
页数：19
相关论文
共 41 条
  • [1] Equivalent projectors for virtual element methods
    Ahmad, B.
    Alsaedi, A.
    Brezzi, F.
    Marini, L. D.
    Russo, A.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (03) : 376 - 391
  • [2] A STREAM VIRTUAL ELEMENT FORMULATION OF THE STOKES PROBLEM ON POLYGONAL MESHES
    Antonietti, P. F.
    da Veiga, L. Beirao
    Mora, D.
    Verani, M.
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2014, 52 (01) : 386 - 404
  • [3] The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations
    Auricchio, F.
    da Veiga, L. Beirao
    Lovadina, C.
    Reali, A.
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (5-8) : 314 - 323
  • [4] SUPG stabilization for the nonconforming virtual element method for advection-diffusion-reaction equations
    Berrone, S.
    Borio, A.
    Manzini, G.
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2018, 340 : 500 - 529
  • [5] Brenner S., 2008, Texts in Applied Mathematics, V3rd ed
  • [6] Virtual element methods on meshes with small edges or faces
    Brenner, Susanne C.
    Sung, Li-Yeng
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2018, 28 (07) : 1291 - 1336
  • [7] Some Estimates for Virtual Element Methods
    Brenner, Susanne C.
    Guan, Qingguang
    Sung, Li-Yeng
    [J]. COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2017, 17 (04) : 553 - 574
  • [8] BASIC PRINCIPLES OF MIXED VIRTUAL ELEMENT METHODS
    Brezzi, F.
    Falk, Richard S.
    Marini, L. Donatella
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2014, 48 (04): : 1227 - 1240
  • [9] A mixed virtual element method for the Brinkman problem
    Caceres, Ernesto
    Gatica, Gabriel N.
    Sequeira, Filander A.
    [J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2017, 27 (04) : 707 - 743
  • [10] A mixed virtual element method for the pseudostress-velocity formulation of the Stokes problem
    Caceres, Ernesto
    Gatica, Gabriel N.
    [J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2017, 37 (01) : 296 - 331
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