Numerical Algorithms

, Volume 60, Issue 4, pp 631–650 | Cite as

Dispersion analysis of triangle-based spectral element methods for elastic wave propagation

Original Paper


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


Elastic wave equation Spectral element methods Triangular grids Dispersion/dissipation analysis 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Politecnico di MilanoMOX-Modelling and Scientific ComputingMilanoItaly
  2. 2.LJAD-Laboratoire de Mathématiques “J.A. Dieudonné”, UMR 7351 UNSA/CNRSUniversité de Nice Sophia-AntipolisNice, Cedex 02France

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