  We consider semi-discrete discontinuous Galerkin approximations of a general
elastodynamics problem, in both {\it displacement} and {\it
displacement-stress} formulations. We present the stability analysis of all the
methods in the natural energy norm and derive optimal a-priori error estimates.
For the displacement-stress formulation, schemes preserving the total energy of
the system are introduced and discussed. We include some numerical experiments
in three dimensions to verify the theory.

Numerical Analysis