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
  • [21] Space-time mesh refinement for the elastodynamic equations
    Bécache, E
    Joly, P
    Rodríguez, J
    [J]. MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, WAVES 2003, 2003, : 313 - 318
  • [22] A space-time discontinuous Galerkin method for the incompressible Navier-Stokes equations
    Rhebergen, Sander
    Cockburn, Bernardo
    van der Vegt, Jaap J. W.
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 233 : 339 - 358
  • [23] Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
    Klaij, C. M.
    van der Vegt, J. J. W.
    van der Ven, H.
    [J]. JOURNAL OF COMPUTATIONAL PHYSICS, 2006, 217 (02) : 589 - 611
  • [24] An Explicit Nodal Space-Time Discontinuous Galerkin Method for Maxwell's Equations
    Angulo, L. D.
    Alvarez, Jesus
    Fernandez Pantoja, Mario
    Gonzalez Garcia, Salvador
    [J]. IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, 2014, 24 (12) : 827 - 829
  • [25] Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations
    Hongling Hu
    Chuanmiao Chen
    Shufang Hu
    Kejia Pan
    [J]. Calcolo, 2021, 58
  • [26] Superconvergence of the space-time discontinuous Galerkin method for linear nonhomogeneous hyperbolic equations
    Hu, Hongling
    Chen, Chuanmiao
    Hu, Shufang
    Pan, Kejia
    [J]. CALCOLO, 2021, 58 (02)
  • [27] Fourierization of the Legendre-Galerkin method and a new space-time spectral method
    Shen, Jie
    Wang, Li-Lian
    [J]. APPLIED NUMERICAL MATHEMATICS, 2007, 57 (5-7) : 710 - 720
  • [28] The Cauchy problem for space-time monopole equations in Sobolev spaces
    Huh, Hyungjin
    Yim, Jihyun
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2018, 59 (04)
  • [29] Spectral Galerkin method for stochastic wave equations driven by space-time white noise
    Cao, Yanzhao
    Yin, Li
    [J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2007, 6 (03) : 607 - 617
  • [30] A new space-time mesh refinement method for Maxwell's equation
    Collino, F
    Fouquet, T
    Joly, P
    [J]. FIFTH INTERNATIONAL CONFERENCE ON MATHEMATICAL AND NUMERICAL ASPECTS OF WAVE PROPAGATION, 2000, : 787 - 791
12345