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On a type of Signorini problem without friction in linear thermoelasticity. (English) Zbl 0534.73095

(Author’s summary.) - In the paper the Signorini problem without friction in linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, the physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and uniqueness of the solution as well as its finite element approximation is proved. It is known that the convergence of the approximate FEM solution to the exact solution is of the order O(h), assuming that the solution is sufficiently regular.
Reviewer: J.Lovíšek

MSC:

74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
49J40 Variational inequalities
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References:

[1] J. Nedoma: Thermo-elastic stress-strain analysis of the geodynamic mechanism. Gerlands Beitr. Geophysik, Leipzig 91 (1982) 1, 75-89.
[2] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Praha 1967. · Zbl 1225.35003
[3] I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics. Aplikace Matematiky, 22 (1977), 215-228. · Zbl 0369.65031
[4] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Aplikace matematiky 22 (1977), 14-51.
[5] U. Mosco G. Strang: One-sided approximation and variational inequalities. Bull. Amer. Math. Soc. 80 (1974), 308-312. · Zbl 0278.35026
[6] R. S. Falk: Error estimates for approximation of a class of a variational inequalities. Math. of Comp. 28 (1974), 963-971. · Zbl 0297.65061
[7] J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary. Aplikace matematiky 22 (1977), 180-188. · Zbl 0434.65083
[8] J. Céa: Optimisation, théorie et algorithmes. Dunod Paris 1971. · Zbl 0211.17402
[9] J. Nedoma: The use of the variational inequalities in geophysics. Proc. of the summer school ”Software and algorithms of numerical mathematics” (Czech), Nové Město n. M., 1979, MFF UK, Praha 1980, 97-100.
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