Structure analysis of higher‐order variational integrators and implementation of SUNDMAN adaptivity in time

Abstract

In this paper, we investigate the use of different higher‐order polynomial bases for the temporal approximation as well as various higher‐order quadrature rules. The resulting time integration schemes partially differ in their numerical properties, especially in order convergence and energy error. Further, an adaptivity of the time increment to optimize the computational effort is implemented using a time transformation according to SUNDMAN. Using an example with viscoelastic material behavior that models a bungee jumper, we show its advantages to minimize the energy error. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)