Abstract
The aim of this paper is to devise an adaptive timestep control in the contact-stabilized Newmark method (ContacX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini’s condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact-stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.
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This research was supported by the DFG Research Center Matheon, “Mathematics for key technologies: Modelling, simulation, and optimization of real-world processes”, Berlin.
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Klapproth, C., Schiela, A. & Deuflhard, P. Adaptive timestep control for the contact-stabilized Newmark method. Numer. Math. 119, 49–81 (2011). https://doi.org/10.1007/s00211-011-0374-3
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DOI: https://doi.org/10.1007/s00211-011-0374-3