Adaptive Timestep Control for the Contact-Stabilized Newmark Method

Please always quote using this URN: urn:nbn:de:0297-zib-11714
  • 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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Author:Corinna Klapproth, Anton Schiela, Peter Deuflhard
Document Type:ZIB-Report
Tag:adaptivity; contact--stabilized Newmark method; dynamical contact problems; extrapolation methods; timestep control
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L86 Nonlinear hyperbolic unilateral problems and nonlinear hyperbolic variational inequalities [See also 35R35, 49J40]
Date of first Publication:2010/06/09
Series (Serial Number):ZIB-Report (10-09)
Published in:Appeared in: Numerische Mathematik vol. 119 iss. 1 (2011), pp. 49-81