Scholarlink

<p>In this paper, we analyze the dispersion and dissipation properties of two fully discrete discontinuous Galerkin (DG) methods, namely the Runge-Kutta DG (RKDG) method and the Lax-Wendroff DG (LWDG) method, when solving the linear convection equation by employing the global spectral analysis (GSA). Under the condition that the convection velocity of the numerical solution is non-constant, we derive the GSA type numerical phase velocity and numerical group velocity through the analysis of the all Fourier waves. Considering that the boundary may be unfitted, we develop an inverse Lax-Wendroff (ILW) boundary treatment for LWDG scheme based on the previous work for RKDG scheme (Yang L, et al. Inverse Lax-Wendroff boundary treatment of discontinuous Galerkin method for 1D conservation laws. <i>Commun. Appl. Math. Comput.</i>, 7, 796–826 (2025)) and make conservation corrections. Finally, we analyze the dispersion properties of the two DG schemes employing the ILW boundary treatment near the boundary, comparing the impact of the boundary treatment. A series of numerical examples verify our theoretical results.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Global Spectral Analysis of Two Fully Discrete Discontinuous Galerkin Methods on Unfitted Meshes

  • 期刊论文

  • 发表日期：

    2025年10月3日

查看全文
  • Hu Yu,
  • Ziqiang Cheng,
  • Yan Jiang

摘要

In this paper, we analyze the dispersion and dissipation properties of two fully discrete discontinuous Galerkin (DG) methods, namely the Runge-Kutta DG (RKDG) method and the Lax-Wendroff DG (LWDG) method, when solving the linear convection equation by employing the global spectral analysis (GSA). Under the condition that the convection velocity of the numerical solution is non-constant, we derive the GSA type numerical phase velocity and numerical group velocity through the analysis of the all Fourier waves. Considering that the boundary may be unfitted, we develop an inverse Lax-Wendroff (ILW) boundary treatment for LWDG scheme based on the previous work for RKDG scheme (Yang L, et al. Inverse Lax-Wendroff boundary treatment of discontinuous Galerkin method for 1D conservation laws. Commun. Appl. Math. Comput., 7, 796–826 (2025)) and make conservation corrections. Finally, we analyze the dispersion properties of the two DG schemes employing the ILW boundary treatment near the boundary, comparing the impact of the boundary treatment. A series of numerical examples verify our theoretical results.