The Contact-Stabilized Newmark Method - Consistency Error of a Spatiotemporal Discretization

Please always quote using this URN: urn:nbn:de:0297-zib-15198
  • The paper considers an improved variant of the contact-stabilized Newmark method by Deuflhard et al., which provides a spatiotemporal numerical integration of dynamical contact problems between viscoelastic bodies in the frame of the Signorini condition. Up no 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 focusses 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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Author:Corinna Klapproth
Document Type:ZIB-Report
Tag:dynamical contact problems, contact-stabilized Newmark method, consistency error
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40]
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M15 Error bounds
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H15 Numerical approximation of solutions
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Mxx Special kinds of problems / 74M15 Contact
Date of first Publication:2012/04/26
Series (Serial Number):ZIB-Report (12-18)