On a type of Signorini problem without friction in linear thermoelasticity

Jiří Nedoma

Aplikace matematiky (1983)

  • Volume: 28, Issue: 6, page 393-407
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Nedoma, Jiří. "On a type of Signorini problem without friction in linear thermoelasticity." Aplikace matematiky 28.6 (1983): 393-407. <http://eudml.org/doc/15320>.

@article{Nedoma1983,
abstract = {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.},
author = {Nedoma, Jiří},
journal = {Aplikace matematiky},
keywords = {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; Signorini problem without friction; linear thermoelasticity; steady-state case; model geodynamical problem; plate tectonic hypothesis; existence; convergence of approximate FEM solution; of order O(h); sufficiently regular solution},
language = {eng},
number = {6},
pages = {393-407},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a type of Signorini problem without friction in linear thermoelasticity},
url = {http://eudml.org/doc/15320},
volume = {28},
year = {1983},
}

TY - JOUR
AU - Nedoma, Jiří
TI - On a type of Signorini problem without friction in linear thermoelasticity
JO - Aplikace matematiky
PY - 1983
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 6
SP - 393
EP - 407
AB - 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.
LA - eng
KW - 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; Signorini problem without friction; linear thermoelasticity; steady-state case; model geodynamical problem; plate tectonic hypothesis; existence; convergence of approximate FEM solution; of order O(h); sufficiently regular solution
UR - http://eudml.org/doc/15320
ER -

References

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  1. J. Nedoma, Thermo-elastic stress-strain analysis of the geodynamic mechanism, Gerlands Beitr. Geophysik, Leipzig 91 (1982) 1, 75-89. (1982) 
  2. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584
  3. I. Hlaváček J. Lovíšek, A finite element analysis for the Signorini problem in plane elastostatics, Aplikace Matematiky, 22 (1977), 215-228. (1977) Zbl0369.65031MR0446014
  4. I. Hlaváček, Dual finite element analysis for unilateral boundary value problems, Aplikace matematiky 22 (1977), 14-51. (1977) Zbl0416.65070MR0426453
  5. U. Mosco G. Strang, 10.1090/S0002-9904-1974-13477-4, Bull. Amer. Math. Soc. 80 (1974), 308-312. (1974) Zbl0278.35026MR0331818DOI10.1090/S0002-9904-1974-13477-4
  6. R. S. Falk, Error estimates for approximation of a class of a variational inequalities, Math. of Соmр. 28 (1974), 963-971. (1974) Zbl0297.65061MR0391502
  7. J. Haslinger, Finite element analysis for unilateral problems with obstacles on the boundary, Aplikace matematiky 22 (1977), 180-188. (1977) Zbl0434.65083MR0440956
  8. J. Céa, Optimisation, théorie et algorithmes, Dunod Paris 1971. (1971) Zbl0211.17402MR0298892
  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. (1979) 

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