| Title:
|
Convergence of dual finite element approximations for unilateral boundary value problems (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
25 |
| Issue:
|
5 |
| Year:
|
1980 |
| Pages:
|
375-386 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author's results on error estimates, no assumption of this kind is imposed here and still the $L^2$-convergence is proved. (English) |
| Keyword:
|
dual finite element approximations |
| Keyword:
|
unilateral boundary value problems |
| Keyword:
|
convergence |
| MSC:
|
35J05 |
| MSC:
|
65N30 |
| MSC:
|
74A55 |
| MSC:
|
74M15 |
| idZBL:
|
Zbl 0462.65064 |
| idMR:
|
MR0590491 |
| DOI:
|
10.21136/AM.1980.103872 |
| . |
| Date available:
|
2008-05-20T18:15:10Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103872 |
| . |
| Reference:
|
[1] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Apl. mat. 22 (1977), 14-51. MR 0426453 |
| Reference:
|
[2] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary I.Apl. mat. 22 (1977), 244-255. MR 0440958 |
| Reference:
|
[3] I. Hlaváček: Dual finite element analysis for semi-coercive unilateral boundary value problems.Apl. mat. 23 (1978), 52-71. MR 0480160 |
| Reference:
|
[4] J. Haslinger, and I. Hlaváček: Convergence of a finite element method based on the dual variaional formulation.Apl. mat. 21 (1976), 43 - 65. MR 0398126 |
| Reference:
|
[5] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892 |
| Reference:
|
[6] I. Hlaváček, J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics.Apl. mat. 22 (1.977), 215 - 228. MR 0446014 |
| Reference:
|
[7] G. Fichera: Boundary value problems of elasticity with unilateral constraints.Encycl. of Physics (ed. by S. Fliigge), vol. VIa/2, Springer- Verlag, Berlin, 1972. |
| Reference:
|
[8] J. Frehse: Regularity of solutions for problems with thin obstacles.Math. Zeitschrift 143 (1975), 279-288. 10.1007/BF01214380 |
| Reference:
|
[9] P. Grisvard, G. Iooss: Problèmes aux limites unilatéraux dans les domaines non réguliers.Publ. Seminaires Math., Univ. de Rennes, 1976. |
| Reference:
|
[10] I. Hlaváček: Convergence of an equilibrium finite element model for plane elastostatics.Apl. mat. 24 (1979), 427-457. MR 0547046 |
| . |
