Analysis of the MAC scheme for the three dimensional Stokes problem

被引：5
|
作者：
Xu, Minqiang [1 ]
Liu, Kai [2 ]
Zhang, Lei [1 ]
机构：
[1] Zhejiang Univ Technol, Coll Sci, Hangzhou 310023, Peoples R China
[2] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
来源：
APPLIED NUMERICAL MATHEMATICS | 2023年 / 193卷
基金：
中国国家自然科学基金;
关键词：
MAC; FVEM; 3D-Stokes equations; Superconvergence; Optimal error estimate; FINITE-ELEMENT-METHOD; EQUATIONS; SUPERCONVERGENCE; CONVERGENCE;
D O I：
10.1016/j.apnum.2023.07.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a marker and cell method (MAC) with a proper quadrature scheme over non-uniform cuboid grids by using a staggered finite volume element method (FVEM) for 3D Stokes equations. The stability of the proposed MAC scheme is proven under Petrov-Galerkin method. By establishing a connection between MAC and FVEM, we rigorously prove the superconvergence property and the optimal order L2 error estimate. Finally, numerical results verify our theoretical findings.& COPY; 2023 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：131 / 147
页数：17
相关论文
共 50 条
  • [1] Superconvergence Analysis of the MAC Scheme for the Two Dimensional Stokes Problem
    Lin, Yanping
    Zou, Qingsong
    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2016, 32 (06) : 1647 - 1666
  • [2] Analysis and convergence of a MAC-like scheme for the generalized Stokes problem
    Numer Methods Partial Differential Equations, 2 (147):
  • [3] Convergence of the MAC Scheme for the Stokes/Darcy Coupling Problem
    Ming-Cheng Shiue
    Kian Chuan Ong
    Ming-Chih Lai
    Journal of Scientific Computing, 2018, 76 : 1216 - 1251
  • [4] Convergence of the MAC Scheme for the Stokes/Darcy Coupling Problem
    Shiue, Ming-Cheng
    Ong, Kian Chuan
    Lai, Ming-Chih
    JOURNAL OF SCIENTIFIC COMPUTING, 2018, 76 (02) : 1216 - 1251
  • [5] Optimal smoothing factor with coarsening by a factor of three for the MAC scheme for the Stokes equations
    He, Yunhui
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2023, 132 : 63 - 72
  • [6] Three Dimensional Flux Problem for the Navier - Stokes Equations
    Pukhnachev, V. V.
    BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2015, 8 (02): : 95 - 104
  • [7] CONVERGENCE OF THE MAC SCHEME FOR THE COMPRESSIBLE STOKES EQUATIONS
    Eymard, R.
    Gallouet, T.
    Herbin, R.
    Latche, J. -C.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (06) : 2218 - 2246
  • [8] A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy
    Boon, Wietse M.
    Glaeser, Dennis
    Helmig, Rainer
    Weishaupt, Kilian
    Yotov, Ivan
    COMPUTATIONAL GEOSCIENCES, 2024, 28 (03) : 413 - 430
  • [9] Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations
    Long Chen
    Ming Wang
    Lin Zhong
    Journal of Scientific Computing, 2015, 63 : 716 - 744
  • [10] Convergence Analysis of Triangular MAC Schemes for Two Dimensional Stokes Equations
    Chen, Long
    Wang, Ming
    Zhong, Lin
    JOURNAL OF SCIENTIFIC COMPUTING, 2015, 63 (03) : 716 - 744
12345