Two-Grid Method for Burgers' Equation by a New Mixed Finite Element Scheme

被引：10
|
作者：
Hu, Xiaohui [1 ]
Huang, Pengzhan [1 ]
Feng, Xinlong [1 ]
机构：
[1] Xinjiang Univ, Urumqi 830046, Peoples R China
来源：
MATHEMATICAL MODELLING AND ANALYSIS | 2014年 / 19卷 / 01期
基金：
中国博士后科学基金;
关键词：
Burgers' equation; two-grid method; stable conforming finite element; Crank-Nicolson scheme; inf sup condition; SEMILINEAR ELLIPTIC-EQUATIONS; TIME-STEPPING STRATEGY; DIFFUSION EQUATIONS;
D O I：
10.3846/13926292.2014.892902
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we present two-grid stable mixed finite element method for the 2D Burgers' equation approximated by the P-0(2) - P-1 pair which satisfies the inf-sup condition. This method consists in dealing with the nonlinear system on a coarse mesh with width H and the linear system on a fine mesh with width h << H by using Crank-Nicolson time-discretization scheme. Our results show that if we choose H-2 = h this method can achieve asymptotically optimal approximation. Error estimates are derived in detail. Finally, numerical experiments show the efficiency of our proposed method and justify the theoretical results.
引用
收藏
页码：1 / 17
页数：17
相关论文
共 50 条
  • [21] A two-grid immersed finite element method with the Crank-Nicolson time scheme for semilinear parabolic interface problems
    Yi, Huaming
    Chen, Yanping
    Wang, Yang
    Huang, Yunqing
    APPLIED NUMERICAL MATHEMATICS, 2023, 189 : 1 - 22
  • [22] Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics
    Hanzhang Hu
    Numerical Algorithms, 2022, 89 : 611 - 636
  • [23] Analysis of two-grid discretization scheme for semilinear hyperbolic equations by mixed finite element methods
    Wang, Keyan
    Chen, Yanping
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (09) : 3370 - 3391
  • [24] TWO-GRID FINITE ELEMENT METHOD FOR TIME-FRACTIONAL NONLINEAR SCHRODINGER EQUATION
    Hu, Hanzhang
    Chen, Yanping
    Zhou, Jianwei
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2024, 42 (04): : 1124 - 1144
  • [25] An efficient nonconforming finite element two-grid method for Allen-Cahn equation
    Shi Dongyang
    Liu Qian
    APPLIED MATHEMATICS LETTERS, 2019, 98 : 374 - 380
  • [26] A TWO-GRID MULTIPOINT FLUX MIXED FINITE ELEMENT METHOD FOR NONLINEAR PARABOLIC PROBLEMS
    Xu, Wenwen
    Li, Xindong
    Song, Nana
    Yang, Lu
    Yuan, Xiqian
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2025, 15 (03): : 1310 - 1329
  • [27] Numerical solution of two-dimensional nonlinear Schrodinger equation using a new two-grid finite element method
    Hu, Hanzhang
    Chen, Yanping
    JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 364
  • [28] A CHARACTERISTIC MIXED FINITE ELEMENT TWO-GRID METHOD FOR COMPRESSIBLE MISCIBLE DISPLACEMENT PROBLEM
    Hu, Hanzhang
    Chen, Yanping
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2022, 40 (05): : 798 - 817
  • [29] Two-grid method for the two-dimensional time-dependent Schrodinger equation by the finite element method
    Tian, Zhikun
    Chen, Yanping
    Huang, Yunqing
    Wang, Jianyun
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 77 (12) : 3043 - 3053
  • [30] Two-Grid Finite Volume Element Method Combined with Crank-Nicolson Scheme for Semilinear Parabolic Equations
    Lou, Yuzhi
    Chen, Chuanjun
    Xue, Guanyu
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (04) : 892 - 913
12345