Timestepping schemes based on discontinuous Galerkin methods

In nonsmooth dynamical systems, state trajectories may be classified in impulsive and non-impulsive periods. There are two types of integration schemes which can handle both types of motion. On the one hand, event-driven methods are highly recommendable in non-impulsive periods e.g. because of their high integration order. However, they cannot represent an infinite accumulation of impacts. On the other hand, classic timestepping schemes are applicable in impulsive periods but they are of integration order one in both impulsive and non-impulsive periods. An enhancement of classic timestepping schemes based on discontinuous Galerkin methods and split-ting of non-impulsive and impulsive force propagation has been presented recently [1]. It benefits from the advantages of event-driven and classic timestepping methods and avoids their disadvantages. A typical representative is the explicit trapezoidal-rule type timestepping method, called D − linear timestepping method. In this talk, we first revisit the basic idea of the D − linear timestepping method in particular. Thereby we assume that ansatz and test functions for the velocity might have jumps across discretization intervals, and that they are of higher integration order inside discretization intervals. Further by splitting contact and impact reactions, contact forces benefit from higher order ansatz functions an