The Signorini-Moreau contact conditions are set as equations by using unknown Level-Set fields. From this, a mixed weak-strong formulation of dynamic contact problems is derived; the Level-Set fields being the intrinsic contact unknown fields. The problem is then discretized by time, space and collocation schemes and some numerical experimentations are carried out, showing the effectiveness of our global approach. The paper is ended with a prospective use of the local multiscale Arlequin method.