  This article considers a unilateral contact problem for the wave equation.
The problem is reduced to a variational inequality for the Dirichlet-to-Neumann
operator for the wave equation on the boundary, which is solved in a saddle
point formulation using boundary elements in the time domain. As a model
problem, also a variational inequality for the single layer operator is
considered. A priori estimates are obtained for Galerkin approximations both to
the variational inequality and the mixed formulation in the case of a flat
contact area, where the existence of solutions to the continuous problem is
known. Numerical experiments demonstrate the performance of the proposed mixed
method. They indicate the stability and convergence beyond flat geometries.
