  We show that applying a classical Schwarz method to the time harmonic Navier
equations, which are an important model for linear elasticity, leads in general
to a divergent method for low to intermediate frequencies. This is even worse
than for Helmholtz and time harmonic Maxwell's equations, where the classical
Schwarz method is also not convergent, but low frequencies only stagnate, they
do not diverge. We illustrate the divergent modes by numerical examples, and
also show that when using the classical Schwarz method as a preconditioner for
a Krylov method, convergence difficulties remain.
