This paper presents a quantitative dispersion-dissipation and stability analysis of the triangle-based discontinuous Galerkin method (DGM) for simulating elastic wave propagation. The analysis is carried out for both P- and S-waves, with semi-discrete and fully discrete cases. The DGM is based on the 1st-order hyperbolic system with numerical flux formulations. The semi-discrete analysis is considered with respect to different numerical fluxes, different mesh configurations, and various ratios of P-wave velocity ($V_p$) and S-wave velocity ($V_s$). The LLF numerical flux and Godunov numerical flux are employed for the analysis. We consider two triangular mesh configurations, which are compared with the quadrilateral mesh. A fully discrete analysis is also presented where 3rd-order total variation diminishing Runge-Kutta temporal discretization is used. The results demonstrate that the numerical dispersion and dissipation vary significantly with the mesh configurations, but they show small difference with respect to the $V_p$ /$V_s$ values. In addition, the performance of LLF flux is similar to that of Godunov flux.

本文介绍了基于三角形的不连续伽勒金方法（DGM）来模拟弹性波传播的定量色散耗散和稳定性分析。对于半离散和完全离散的情况，都对P波和S波进行了分析。DGM基于带有数值通量公式的一阶双曲系统。对于不同的数值通量，不同的网格配置以及各种P波速比（$V_p$）和S波速度（$V_s$）。分析采用LLF数值通量和Godunov数值通量。我们考虑两个三角形网格配置，将它们与四边形网格进行比较。还提出了使用三阶总方差减小Runge-Kutta时间离散化的完全离散分析。结果表明，数值色散和耗散随网格配置的不同而有很大差异，但相对于网格，它们显示出很小的差异。$V_p$ /$V_s$价值观。此外，LLF通量的性能类似于Godunov通量。