Evolutionary Variational Inequalities Arising in Viscoelastic Contact Problems

We consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials. Under the smallness assumption of a certain coefficient, we prove an existence and uniqueness result using Banach's fixed point theorem. We then study two nume...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2000-01, Vol.38 (2), p.556-579
Main Authors: Han, Weimin, Sofonea, Mircea
Format: Article
Language:English
Subjects:
Applied mathematics
Approximation
Awns
Cauchy problems
Diagonal lemma
Error rates
Exact sciences and technology
Finite element method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Hilbert spaces
Inelasticity (thermoplasticity, viscoplasticity...)
Inequality
Mathematical inequalities
Mathematics
Non-newtonian fluid flows
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Sciences and techniques of general use
Social evolution
Solid mechanics
Structural and continuum mechanics
Uniqueness
Variational inequalities
Viscoelasticity
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Summary:We consider a class of evolutionary variational inequalities arising in various frictional contact problems for viscoelastic materials. Under the smallness assumption of a certain coefficient, we prove an existence and uniqueness result using Banach's fixed point theorem. We then study two numerical approximation schemes of the problem: a semidiscrete scheme and a fully discrete scheme. For both schemes, we show the existence of a unique solution and derive error estimates. Finally, all these results are applied to the analysis and numerical approximations of a viscoelastic frictional contact problem, with the finite element method used to discretize the spatial domain.
ISSN:0036-1429
1095-7170
DOI:10.1137/s0036142998347309