Abstract
The paper considers a slightly improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatio-temporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up to 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.
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Acknowledgments
The author thanks Anton Schiela, Technical University of Berlin, and especially Peter Deuflhard, Zuse Institute Berlin, for helpful discussions on the topic of this paper.
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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. The contact-stabilized Newmark method: consistency error of a spatiotemporal discretization. Numer. Math. 131, 59–82 (2015). https://doi.org/10.1007/s00211-014-0686-1
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DOI: https://doi.org/10.1007/s00211-014-0686-1