The contact-stabilized Newmark method: consistency error of a spatiotemporal discretization

The paper considers an improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatiotemporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up no now, the question of consistency in the case of contact constraints has been discussed for time integrators in function space under the assumption of bounded total variation of the solution. Here, interest focuses on the consistency error of the Newmark scheme in physical energy norm after discretization both in time and in space. The resulting estimate for the local discretization error allows to prove global convergence of the Newmark scheme under an additional assumption on the active contact boundaries. AMS MSC 2000: 35L85, 65M15, 74H15, 74M15