Dynamic obstacle and Signorini problems are discretised by continuous
and discontinuous finite elements in space and time. The resulting
discrete problems are attributed to a standard implicit time stepping
scheme through relaxation of impact phenomena and suitable numerical
integration. The method can cope with dynamic contact problems, which
is shown by an analysis of a model problem. Moreover, numerical examples
demonstrate that it is actually able to approximate the solution of
dynamic contact problems, which are not fully covert by the theory.