Dispersion-dissipation analysis of 3D continuous and discontinuous spectral element methods for the elastodynamics equation

In this paper we present a three dimensional dispersion and dissipation analysis for both the semi discrete and the fully discrete approximation of the elastodynamics equation based on the plane wave method. For space discretization we compare different approximation strategies, namely the continuous and the discontinuous spectral element method on both tetrahedral and hexahedral elements. For time discretization we employ a leapfrog time integration scheme. Several numerical results are presented and discussed.