A new space-time continuous Galerkin method with mesh modification for Sobolev equations

被引：15
|
作者：
Zhao, Zhihui [1 ]
Li, Hong [1 ]
Luo, Zhendong [2 ]
机构：
[1] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China
[2] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2016年 / 440卷 / 01期
基金：
美国国家科学基金会;
关键词：
Continuous Galerkin method; Sobolev equations; Optimal rates of convergence; Numerical examples; FINITE-ELEMENT-METHOD; NONLINEAR SCHRODINGER-EQUATION;
D O I：
10.1016/j.jmaa.2016.03.035
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this study, we first propose the continuous Galerkin (CG) method for the Sobolev equations, which allows different temporal step-sizes and spatial grids in each time step. And then, we demonstrate the existence and uniqueness of the approximate solutions and derive the optimal rates of convergence of the approximate solutions under the restrictive assumptions that the space time finite element subspaces between two successive time steps are conforming elements. Finally, we provide some numerical examples on unstructured meshes to demonstrate the efficiency and flexibility of this method. (C) 2016 Elsevier Inc. All rights reserved.
引用
收藏
页码：86 / 105
页数：20
相关论文
共 50 条
  • [1] A space-time continuous Galerkin method with mesh modification for viscoelastic wave equations
    Zhao, Zhihui
    Li, Hong
    Luo, Zhendong
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2017, 33 (04) : 1183 - 1207
  • [2] Analysis of a space-time continuous Galerkin method for convection-dominated Sobolev equations
    Zhao, Zhihui
    Li, Hong
    Luo, Zhendong
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (08) : 1643 - 1656
  • [3] Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations
    He, Siriguleng
    Li, Hong
    Liu, Yang
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2013, 8 (04) : 825 - 836
  • [4] Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations
    Siriguleng He
    Hong Li
    Yang Liu
    [J]. Frontiers of Mathematics in China, 2013, 8 : 825 - 836
  • [5] Numerical analysis of a space-time continuous Galerkin method for the nonlinear Sobolev equation
    Zhao, Zhihui
    Li, Hong
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 531 (02)
  • [6] The study of a continuous Galerkin method for Sobolev equation with space-time variable coefficients
    Zhao, Zhihui
    Li, Hong
    Wang, Jing
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2021, 401 (401)
  • [7] A space-time discontinuous Galerkin method for linear convection-dominated Sobolev equations
    Sun, Tongjun
    Ma, Keying
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 210 (02) : 490 - 503
  • [8] Convergence of a continuous Galerkin method with mesh modification for nonlinear wave equations
    Karakashian, O
    Makridakis, C
    [J]. MATHEMATICS OF COMPUTATION, 2005, 74 (249) : 85 - 102
  • [9] Convergence of a space-time continuous Galerkin method for the wave equation
    Zhao, Zhihui
    Li, Hong
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
  • [10] Space-Time Discontinuous Galerkin Method for Maxwell's Equations
    Xie, Ziqing
    Wang, Bo
    Zhang, Zhimin
    [J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2013, 14 (04) : 916 - 939
12345