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Consistency results on Newmark methods for dynamical contact problems

Title data

Klapproth, Corinna ; Schiela, Anton ; Deuflhard, Peter:
Consistency results on Newmark methods for dynamical contact problems.
In: Numerische Mathematik. Vol. 116 (2010) Issue 1 . - pp. 65-94.
ISSN 0029-599X
DOI: https://doi.org/10.1007/s00211-010-0300-0

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Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

The paper considers the time integration of frictionless dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Among the numerical integrators, interest focuses on the classical Newmark method, the improved energy dissipative version due to Kane et al., and the contact-stabilized Newmark method recently suggested by Deuflhard et al. In the absence of contact, any such variant is equivalent to the Störmer-Verlet scheme, which is well-known to have consistency order 2. In the presence of contact, however, the classical approach to discretization errors would not show consistency at all because of the discontinuity at the contact. Surprisingly, the question of consistency in the constrained situation has not been solved yet. The present paper fills this gap by means of a novel proof technique using specific norms based on earlier perturbation results due to the authors. The corresponding estimation of the local discretization error requires the bounded total variation of the solution. The results have consequences for the construction of an adaptive timestep control, which will be worked out subsequently in a forthcoming paper.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version under the title "Consistency Results for the Contact-Stabilized Newmark Method" is published at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 09-06.
Keywords: dynamical contact problems; Newmark method; Signorini condition; consistency; viscoelasticity
Subject classification: 35L85 (74M15 74H15 65J15)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 17 Mar 2015 09:43
Last Modified: 17 Mar 2015 09:43
URI: https://eref.uni-bayreuth.de/id/eprint/8050