| Title:
|
Dual finite element analysis for elliptic problems with obstacles on the boundary. I (English) |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
22 |
| Issue:
|
4 |
| Year:
|
1977 |
| Pages:
|
244-255 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
For an elliptic model problem with non-homogeneous unilateral boundary conditions, two dual variational formulations are presented and justified on the basis of a saddle point theorem. Using piecewise linear finite element models on the triangulation of the given domain, dual numerical procedures are proposed. By means of one-sided approximations, some a priori error estimates are proved, assuming that the solution is sufficiently smooth. A posteriori error estimates and two-sided bounds for the energy are also deduced. (English) |
| Keyword:
|
elliptic model problem |
| Keyword:
|
dual variational formulation |
| Keyword:
|
piecewise linear finite elements |
| Keyword:
|
a priori error estimates |
| Keyword:
|
a posteriori error estimates |
| Keyword:
|
two-sided bounds |
| MSC:
|
35J25 |
| MSC:
|
65K10 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0422.65065 |
| idMR:
|
MR0440958 |
| DOI:
|
10.21136/AM.1977.103701 |
| . |
| Date available:
|
2008-05-20T18:07:33Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103701 |
| . |
| Reference:
|
[1] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[2] G. N. Jakovlev: Boundary properties of functions of class $W_p^{(1)}$ on the domains with angular points.(in Russian). DAN SSSR, 140 (1961), 73-76. MR 0136988 |
| Reference:
|
[3] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Aplikace matematiky 22 (1977), 14-51. MR 0426453 |
| Reference:
|
[4] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892 |
| Reference:
|
[5] U. Mosco G. Strang: One-sided approximations and variational inequalities.Bull. Am. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4 |
| Reference:
|
[6] I. Hlaváček: Some equilibrium and mixed models in the finite element method.Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). MR 0514379 |
| . |
