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三阶偏微分方程的时空间断Galerkin谱方法

薛未, 吴华   

  1. 上海大学理学院, 上海 200444
  • 收稿日期:2020-02-19 出版日期:2021-09-15 发布日期:2021-09-17
  • 通讯作者: 吴华,hwu@shu.edu.cn
  • 基金资助:
    国家自然科学基金(11571225)资助.

薛未, 吴华. 三阶偏微分方程的时空间断Galerkin谱方法[J]. 数值计算与计算机应用, 2021, 42(3): 247-262.

Xue Wei, Wu Hua. SPACE-TIME DISCONTINUOUS GALERKIN SPECTRAL METHOD FOR THIRD-ORDER PARTIAL DIFFERENTIAL EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(3): 247-262.

SPACE-TIME DISCONTINUOUS GALERKIN SPECTRAL METHOD FOR THIRD-ORDER PARTIAL DIFFERENTIAL EQUATIONS

Xue Wei, Wu Hua   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2020-02-19 Online:2021-09-15 Published:2021-09-17
本文提出了三阶偏微分方程的时空间断Galerkin谱方法.该方法在空间方向上采用局部间断Galerkin谱方法,即在每个子区域上,该格式按Legendre-Galerkin谱方法形成,子区域交界面处的跳跃项利用数值流量进行处理.在时间方向上采用多区域Legendre-tau谱方法.文中将该全离散格式分别应用到线性与非线性方程中,并分别给出了数值算例.理论分析部分给出了三阶线性偏微分方程在全离散格式下的收敛性分析.
In this paper, space-time discontinuous Galerkin spectral method for third-order partial differential equations is proposed.The local discontinuous Galerkin spectral method is used in the spatial direction, in which numerical schemes in each subdomain are generated using the Legendre-Galerkin method, and those jump terms crossing boundaries of different cells are dealt with using numerical flux.Meanwhile, the Legendre-tau spectral method is used in the time direction.The fully discrete scheme is applied to linear and nonlinear equations, respectively.Examples are given to illustrate their numerical schemes.As theoretical analysis, convergence of the fully discrete scheme for the third-order linear partial differential equations is analyzed.

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