Section: New Results

High-accuracy time-stepping schemes

Participant : Vincent Acary.

To perform the numerical time integration of nonsmooth mechanical systems, the family of event-capturing time–stepping schemes are the most robust and efficient tools. Nevertheless, they suffer from several drawbacks : a) a low–order accuracy (at best at order one), b) a drift phenomena when the unilateral constraints are treated at the velocity level and c) a poor “energetic” behavior in terms of stabilizing the high–frequency dynamics. We fist proposed to improve the global order of accuracy over periods when the evolution is sufficiently smooth by mixing standard higher order schemes for Differential Algebraic equations and the Moreau–Jean's scheme [16] . We also proposed self-adapting schemes by applying time–discontinuous Galerkin methods to the measure differential equation in [24] . In order to satisfy in discrete time, the impact law and the constraints at the position and the velocity level, an adaptation of the well-known Gear–Gupta–Leimkuhler approach has been developed in [17] . Finally, the energetic behavior of the standard Moreau–Jean scheme has been addressed in [25] by developing a Newmark–type scheme for nonsmooth dynamics.