  We prove error estimates for a finite element approximation of viscoelastic
dynamics based on continuous Galerkin in space and time, both in energy norm
and in $L^2$ norm. The proof is based on an error representation formula using
a discrete dual problem and a stability estimate involving the kinetic,
elastic, and viscoelastic energies. To set up the dual error analysis and to
prove the basic stability estimates, it is natural to formulate the problem as
a system involving evolution equations for the viscoelastic stress, the
displacements, and the velocities. The equations for the viscoelastic stress
can, however, be solved analytically in terms of the deviatoric strain
velocity, and therefore, the viscoelastic stress can be eliminated from the
system, resulting in a system for displacements and velocities.
