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Title: On a type of Signorini problem without friction in linear thermoelasticity (English)
Author: Nedoma, Jiří
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 28
Issue: 6
Year: 1983
Pages: 393-407
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: In the paper the Signorini problem without friction in the linear thermoelasticity for the steady-state case is investigated. The problem discussed is the model geodynamical problem, physical analysis of which is based on the plate tectonic hypothesis and the theory of thermoelasticity. The existence and unicity of the solution of the Signorini problem without friction for the steady-state case in the linear thermoelasticity 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. (English)
Keyword: Signorini problem without friction
Keyword: steady-state case
Keyword: model geodynamical problem
Keyword: plate tectonic hypothesis
Keyword: existence
Keyword: convergence of approximate FEM solution
Keyword: of order O(h)
Keyword: sufficiently regular solution
MSC: 49J40
MSC: 73N99
MSC: 73U05
MSC: 74A55
MSC: 74F05
MSC: 74G30
MSC: 74H25
MSC: 74M15
MSC: 74S05
MSC: 74S30
MSC: 86A60
idZBL: Zbl 0534.73095
idMR: MR0723201
DOI: 10.21136/AM.1983.104053
Date available: 2008-05-20T18:23:24Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Nedoma: Thermo-elastic stress-strain analysis of the geodynamic mechanism.Gerlands Beitr. Geophysik, Leipzig 91 (1982) 1, 75-89.
Reference: [2] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Praha 1967. MR 0227584
Reference: [3] I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics.Aplikace Matematiky, 22 (1977), 215-228. MR 0446014
Reference: [4] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Aplikace matematiky 22 (1977), 14-51. MR 0426453
Reference: [5] U. Mosco G. Strang: One-sided approximation and variational inequalities.Bull. Amer. Math. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4
Reference: [6] R. S. Falk: Error estimates for approximation of a class of a variational inequalities.Math. of Соmр. 28 (1974), 963-971. MR 0391502
Reference: [7] J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary.Aplikace matematiky 22 (1977), 180-188. Zbl 0434.65083, MR 0440956
Reference: [8] J. Céa: Optimisation, théorie et algorithmes.Dunod Paris 1971. MR 0298892
Reference: [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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