# Approximation and numerical solution of contact problems with friction

Jaroslav Haslinger; Miroslav Tvrdý

Aplikace matematiky (1983)

- Volume: 28, Issue: 1, page 55-71
- ISSN: 0862-7940

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topHaslinger, Jaroslav, and Tvrdý, Miroslav. "Approximation and numerical solution of contact problems with friction." Aplikace matematiky 28.1 (1983): 55-71. <http://eudml.org/doc/15274>.

@article{Haslinger1983,

abstract = {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 $\mathcal \{L\}$ 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.},

author = {Haslinger, Jaroslav, Tvrdý, Miroslav},

journal = {Aplikace matematiky},

keywords = {suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa’s algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional; suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa's algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional},

language = {eng},

number = {1},

pages = {55-71},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Approximation and numerical solution of contact problems with friction},

url = {http://eudml.org/doc/15274},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Haslinger, Jaroslav

AU - Tvrdý, Miroslav

TI - Approximation and numerical solution of contact problems with friction

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 1

SP - 55

EP - 71

AB - 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 $\mathcal {L}$ 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.

LA - eng

KW - suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa’s algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional; suitable choice of multipliers; saddle-point of Lagrangian function; certain convex set; approximation; rate of convergence; Uzawa's algorithm; plane problem; linear-elastic body; rigid foundation; influence of friction; minimum of non-differentiable functional

UR - http://eudml.org/doc/15274

ER -

## References

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- J. Haslinger I. Hlaváček, Contact between elastic bodies. Part II. Finite element analysis, Apl. Mat. 26 (1981) 324-347. (1981)
- M. Tvrdý, The Signorini problem with friction, Thesis, Fac. Math. Phys., Charles Univ., Prague (in Czech).
- R. Glowinski J. L. Lions R. Trémolières, Analyse numérique des inéquations variationnelles, Dunod, Paris 1976. (1976)
- I. Ekeland R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam 1976. (1976) MR0463994
- J. Haslinger I. Hlaváček, Approximation of the Signorini problem with friction by a mixed finite element method, JMAA, Vol. 86, No. 1, 99-122. MR0649858
- J. Haslinger, Mixed formulation of variational inequalities and its approximation, Apl. Mat. 26 (1981) No. 6. (1981) MR0634283
- B. N. Pšeničnyj J. M. Danilin, Численные методы в экстремальных задачах, Nauka, Moskva 1975. (1975)
- 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. (1979)

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