Mixed boundary value problems for hyperbolic equations and boundary element approximation

The solution to the elastodynamic equations with mixed boundary conditions exhibits a singular behavior where the boundary conditions change. We obtain detailed expansions of the singularities of the Dirichlet trace of the solution and the traction on the boundary. The results imply quasi-optimal estimates for piecewise polynomial approximations. The results are applied to hp and graded versions of the time domain boundary element method. Numerical examples illustrate the theoretical results in 2d. They confirm the expected quasi-optimal convergence rates and the singular behavior of the numerical approximations.