Dispersion analysis of triangle-based spectral elementmethods for elastic wave propagation

We study the numerical dispersion/dissipation of Triangle-based Spectral Element Methods (T SEM) of order N ≥ 1 when coupled with the Leap-Frog (LF) finite difference scheme to simulate the elastic wave propagation over an unstructured triangulation of the 2D physical domain. The analysis relies on the discrete eigenvalue problem resulting from the approximation of the dispersion relation. We present dispersion graphs by varying the approximation polynomial degree, the number of discrete points per wavelength and the time step. Numerical results for the T SEM-LF are compared with those of the LF coupled to the classical Quadrangle-based Spectral Element Method (QSEM).