| Title:
|
On the Signorini problem with friction in linear thermoelasticity: The quasi-coupled 2D-case (English) |
| Author:
|
Nedoma, Jiří |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
3 |
| Year:
|
1987 |
| Pages:
|
186-199 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Signorini problem with friction in quasi-coupled linear thermo-elasticity (the 2D-case) is discussed. The problem is the model problem in the geodynamics. Using piecewise linear finite elements on the triangulation of the given domain, numerical procedures are proposed. The finite element analysis for the Signorini problem with friction on the contact boundary $\Gamma_\alpha$ of a polygonal domain $G\subset R^2$ is given. The rate of convergence is proved if the exact solution is sufficiently regular. (English) |
| Keyword:
|
Signorini problem |
| Keyword:
|
model problem in geodynamics |
| Keyword:
|
simulation of dynamic plate tectonic model |
| Keyword:
|
collision zones |
| Keyword:
|
equilibrium equation |
| Keyword:
|
heat conduction equation |
| Keyword:
|
two-dimensional quasi-steady-state thermoelastic contact problem |
| Keyword:
|
Coulomb friction |
| Keyword:
|
Existence |
| Keyword:
|
uniqueness |
| Keyword:
|
finite element method |
| Keyword:
|
piecewise linear functions |
| Keyword:
|
triangulation |
| Keyword:
|
thermal part |
| Keyword:
|
quadratic programming |
| Keyword:
|
elastic part |
| Keyword:
|
approximation of a saddle point |
| MSC:
|
49J40 |
| MSC:
|
73T05 |
| MSC:
|
73U05 |
| MSC:
|
74A55 |
| MSC:
|
74F05 |
| MSC:
|
74L05 |
| MSC:
|
74M15 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 0631.73098 |
| idMR:
|
MR0895877 |
| DOI:
|
10.21136/AM.1987.104250 |
| . |
| Date available:
|
2008-05-20T18:32:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104250 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
[7] J. Haslinger: Approximation of the Signorini problem with friction obeying the Coulomb law.Math. Meth. in Sci Appl. 5 (1983). Zbl 0525.73130, MR 0716664, 10.1002/mma.1670050127 |
| Reference:
|
[8] J. Haslinger I. Hlaváček: Approximation of the Signorini problem with friction by a mixed element method.J. Math. Anal. Appl. 86 (1983) 1, 99-122, MR 0649858, 10.1016/0022-247X(82)90257-8 |
| Reference:
|
[9] J. Haslinger J. Tvrdý: Approximation and numerical solution of contact problems with friction.Apl. mat. 28 (1983) 1, 55-74. MR 0684711 |
| Reference:
|
[10] I. Hlaváček J. Haslinger J. Nečas J. Lovíšek: Solving Variational Inequalities in Mechanics.(in Slovak). ALFA, Bratislava 1982. |
| Reference:
|
[11] I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostastatics.Apl. mat. 22 (1977), 215-228. MR 0446014 |
| Reference:
|
[12] J. Jarušek: Contact problems with friction.Thesis, MFFUK, Praha 1980 (in Czech). |
| Reference:
|
[13] J. Jarušek: Contact problems with bounded friction. Coercive case.Czech. Math. J. 33 (1983) 2, 237-261. MR 0699024 |
| Reference:
|
[14] J. Jarušek: Contact problems with bounded friction. Semicoercive case.Czech. Math. J. 34 (109) (1984), 619-629. MR 0764444 |
| Reference:
|
[15] J. Nečas J. Jarušek J. Haslinger: On the solution of the variational inequality to the Signorini problem with small friction.Boll. Unione Mat. Ital. (5) 17-B (1980), 796-811. MR 0580559 |
| Reference:
|
[16] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam 1981. MR 0600655 |
| Reference:
|
[17] J. Nedoma: Some mathematical problems of contemporary geodynamics and some of their solution.(manuscript 1979). |
| Reference:
|
[18] J. Nedoma: The use of the variational inequalities in geophysics.Proc. Summer school "Algorithms and software of numerical mathematics" (Nové Město n. M. 1979) MFF UK, Praha 1980 (in Czech). |
| Reference:
|
[19] J. Nedoma: Model of Carpathian Continent/Continent Collision.Symposium on Plate Tectonics of Eastern Europe, EGS-ESC Budapest 8,24-29 August 1980, Budapest 1980. Proc. of the 17th Assembly of the ESC Budapest 1980, 629-637. |
| Reference:
|
[20] J. Nedoma: Variational methods and finite element method in geophysical problems.In: Computational methods in geophysics. Radio i svyaz, Moscow 1981 (in Russian). |
| Reference:
|
[21] J. Nedoma: Thermoelastic stress-strain analysis of the geodynamic mechanism.Gerlands Beitr. Geophysik, Leipzig 91 (1982) 1, 75-89. |
| Reference:
|
[22] J. Nedoma: Contribution to the study of the geotectonic stress field in the region of the West Carpathians:.Proc. of the 2nd Inter. Symposium on the Analysis of Seismicity and on Seismic Hazard, Liblice, Czechoslovakia, May 18-23, 1981, Geoph. Inst, Czech. Acad. Sci, Prague 1982, 321-338. MR 0411367 |
| Reference:
|
[23] J. Nedoma: On one type of Signorini problem without friction in linear thermoelasticity.Apl. mat. 28 (1983) 6, 393-407. MR 0723201 |
| . |
