  We evaluated the performance of the classical and spectral finite element
method in the simulation of elastodynamic problems. We used as a quality
measure their ability to capture the actual dispersive behavior of the
material. Four different materials are studied: a homogeneous non-dispersive
material, a bilayer material, and composite materials consisting of an aluminum
matrix and brass inclusions or voids. To obtain the dispersion properties,
spatial periodicity is assumed so the analysis is conducted using Floquet-Bloch
principles. The effects in the dispersion properties of the lumping process for
the mass matrices resulting from the classical finite element method are also
investigated, since that is a common practice when the problem is solved with
explicit time marching schemes. At high frequencies the predictions with the
spectral technique exactly match the analytical dispersion curves, while the
classical method does not. This occurs even at the same computational demands.
At low frequencies however, the results from both the classical (consistent or
mass-lumped) and spectral finite element coincide with the analytically
determined curves. Surprisingly, at low frequencies even the results obtained
with the artificial diagonal mass matrix from the classical technique exactly
match the analytic dispersion curves.
