A numerical study on continuous space-time Finite Element Methods for dynamic Signorini problems

Space-time nite element methods for dynamic Signorini problems are discussed in this article. The discretization scheme is based on a mixed space-time formulation of the continuous problem, where the Lagrange multipliers represent the contact stress. To construct the trial space for the displacement and the velocity, we use piecewise polynomial and globally continuous basis functions in space and time. It is combined with a test space consisting of piecewise polynomial and possibly discontinuous basis functions in time. The Lagrange multiplier is approximated by piecewise discontinuous polynomials in space and time. By suitable combinations of the polynomial degrees as well as the underlying meshes, we ensure the stability of the presented scheme, which is substantiated by some numerical experiments.