  The solution to the elastodynamic equation in the exterior of a polyhedral
domain or a screen exhibits singular behavior from the corners and edges. The
detailed expansion of the singularities implies quasi-optimal estimates for
piecewise polynomial approximations of the Dirichlet trace of the solution and
the traction. The results are applied to hp and graded versions of the time
domain boundary element method for the weakly singular and the hypersingular
integral equations. Numerical examples confirm the theoretical results for the
Dirichlet and Neumann problems for screens and for polygonal domains in 2d.
They exhibit the expected quasi-optimal convergence rates and the singular
behavior of the solutions.
