| MR 0723201
| Zbl 0534.73095
| DOI: 10.21136/AM.1983.104053
Signorini problem without friction; steady-state case; model geodynamical problem; plate tectonic hypothesis; existence; convergence of approximate FEM solution; of order O(h); sufficiently regular solution
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.
 J. Nedoma: Thermo-elastic stress-strain analysis of the geodynamic mechanism. Gerlands Beitr. Geophysik, Leipzig 91 (1982) 1, 75-89.
 J. Nečas: Les méthodes directes en théorie des équations elliptiques
. Academia, Praha 1967. MR 0227584
 I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics
. Aplikace Matematiky, 22 (1977), 215-228. MR 0446014
 I. Hlaváček: Dual finite element analysis for unilateral boundary value problems
. Aplikace matematiky 22 (1977), 14-51. MR 0426453
 R. S. Falk: Error estimates for approximation of a class of a variational inequalities
. Math. of Соmр. 28 (1974), 963-971. MR 0391502
 J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary
. Aplikace matematiky 22 (1977), 180-188. MR 0440956
| Zbl 0434.65083
 J. Céa: Optimisation, théorie et algorithmes
. Dunod Paris 1971. MR 0298892
 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.