A family of space–time connecting discretization schemes with local impact detection for elastodynamic contact problems

We derive, formulate and analyze a new family of discretization schemes for elastodynamic contact problems which implicitly resolve the individual impact times for each node on the contact interface. Within our approach, information from the space discrete setting is incorporated into the time discretization by means of pointwise chosen parameters for the time discretization scheme. The members of this family can be interpreted as modified Newmark schemes, thus making them easily understandable and implementable. We prove that for certain parameter choices the algorithms are dissipative methods. Further, as our analysis and our numerical experiments show, a special solution dependent choice of parameters leads to a new space–time connecting discretization with a highly stable behavior of displacements, velocities and boundary stresses at the contact interface.