The Cascadic Multigrid Method of the Weak Galerkin Method for Second-Order Elliptic Equation

被引：1
|
作者：
Sun, Shi [1 ]
Huang, Ziping [1 ]
Wang, Cheng [1 ]
Guo, Liming [2 ]
机构：
[1] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China
[2] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China
来源：
MATHEMATICAL PROBLEMS IN ENGINEERING | 2017年 / 2017卷
基金：
美国国家科学基金会;
关键词：
FINITE-ELEMENT METHODS;
D O I：
10.1155/2017/7912845
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
This paper is devoted to the analysis of the cascadic multigrid algorithm for solving the linear system arising from the weak Galerkin finite element method. The proposed cascadic multigrid method is optimal for conjugate gradient iteration and quasi-optimal for Jacobi, Gauss-Seidel, and Richardson iterations. Numerical results are also provided to validate our theoretical analysis.
引用
收藏
页数：8
相关论文
共 50 条
  • [21] A local discontinuous Galerkin method for the second-order wave equation
    Baccouch, Mahboub
    COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 209 : 129 - 143
  • [22] A WEAK GALERKIN MIXED FINITE ELEMENT METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS
    Zhang, Qian
    Zhang, Ran
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2016, 34 (05) : 532 - 548
  • [23] An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems
    Zhang, Xiao
    Xie, Xiaoping
    Zhang, Shiquan
    COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2019, 19 (04) : 849 - 861
  • [24] AN ANALYSIS OF THE EMBEDDED DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC PROBLEMS
    Cockburn, Bernardo
    Guzman, Johnny
    Soon, See-Chew
    Stolarski, Henry K.
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (04) : 2686 - 2707
  • [25] A DEEP LEARNING GALERKIN METHOD FOR THE SECOND-ORDER LINEAR ELLIPTIC EQUATIONS
    Li, Jian
    Zhang, Wen
    Yue, Jing
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2021, 18 (04) : 427 - 441
  • [26] A cascadic multigrid method for a kind of semilinear elliptic problem
    Yu, Haixiong
    Zeng, Jinping
    NUMERICAL ALGORITHMS, 2011, 58 (02) : 143 - 162
  • [27] A cascadic multigrid method for a kind of semilinear elliptic problem
    Haixiong Yu
    Jinping Zeng
    Numerical Algorithms, 2011, 58 : 143 - 162
  • [28] Weak Galerkin method with implicit θ-schemes for second-order parabolic problems
    Qi, Wenya
    Song, Lunji
    APPLIED MATHEMATICS AND COMPUTATION, 2020, 366
  • [29] A penalized weak Galerkin spectral element method for second order elliptic equations
    Pan, Jiajia
    Li, Huiyuan
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 386
  • [30] On the convergence of an extrapolation cascadic multigrid method for elliptic problems
    Hu, Hongling
    Ren, Zhengyong
    He, Dongdong
    Pan, Kejia
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (04) : 759 - 771
12345