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Title: Approximation and numerical solution of contact problems with friction (English)
Author: Haslinger, Jaroslav
Author: Tvrdý, Miroslav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 28
Issue: 1
Year: 1983
Pages: 55-71
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: The present paper deals with numerical solution of the contact problem with given friction. By a suitable choice of multipliers the whole problem is transformed to that of finding a saddle-point of the Lagrangian function $\Cal L$ on a certain convex set $K\times\Lambda$. The approximation of this saddle-point is defined, the convergence is proved and the rate of convergence established. For the numerical realization Uzawa's algorithm is used. Some examples are given in the conclusion. (English)
Keyword: suitable choice of multipliers
Keyword: saddle-point of Lagrangian function
Keyword: certain convex set
Keyword: approximation
Keyword: rate of convergence
Keyword: Uzawa’s algorithm
Keyword: plane problem
Keyword: linear-elastic body
Keyword: rigid foundation
Keyword: influence of friction
Keyword: minimum of non-differentiable functional
MSC: 49J40
MSC: 65N30
MSC: 73-08
MSC: 73T05
MSC: 74A55
MSC: 74G30
MSC: 74H25
MSC: 74M15
MSC: 74S05
MSC: 74S30
MSC: 74S99
idZBL: Zbl 0513.73089
idMR: MR0684711
Date available: 2008-05-20T18:21:03Z
Last updated: 2015-06-18
Stable URL:
Reference: [1] J. Cea: Оптиимзация. Теория и алгорифмы.Mir, Moskva 1973. Zbl 0303.93022
Reference: [2] G. Duvaut J. L. Lions: Les inéquations en mécanique et en physique.Dunod, Paris 1972. MR 0464857
Reference: [3] J. Haslinger I. Hlaváček: Contact between elastic bodies. Part II. Finite element analysis.Apl. Mat. 26 (1981) 324-347.
Reference: [4] M. Tvrdý: The Signorini problem with friction.Thesis, Fac. Math. Phys., Charles Univ., Prague (in Czech).
Reference: [5] R. Glowinski J. L. Lions R. Trémolières: Analyse numérique des inéquations variationnelles.Dunod, Paris 1976.
Reference: [6] I. Ekeland R. Temam: Convex Analysis and Variational Problems.North-Holland, Amsterdam 1976. MR 0463994
Reference: [7] J. Haslinger I. Hlaváček: Approximation of the Signorini problem with friction by a mixed finite element method.JMAA, Vol. 86, No. 1, 99-122. MR 0649858
Reference: [8] J. Haslinger: Mixed formulation of variational inequalities and its approximation.Apl. Mat. 26 (1981) No. 6. MR 0634283
Reference: [9] B. N. Pšeničnyj J. M. Danilin: Численные методы в экстремальных задачах.Nauka, Moskva 1975.
Reference: [10] N. Kikuchi J. T. Oden: Contact problems in elasticity.TICOM Report 79 - 8, July 1979, Texas Inst. for computational mechanics, The University of Texas at Austin.


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