| Title:
|
Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary (English) |
| Author:
|
Tran, Van Bon |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1988 |
| Pages:
|
1-21 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Poisson equation with non-homogeneous unilateral condition on the boundary is solved by means of finite elements. The primal variational problem is approximated on the basis of linear triangular elements, and $O(h)$-convergence is proved provided the exact solution is regular enough. For the dual problem piecewise linear divergence-free approximations are employed and $O(h^{3/2})$-convergence proved for a regular solution. Some a posteriori error estimates are also presented. (English) |
| Keyword:
|
semi-coercive elliptic problems |
| Keyword:
|
Poisson equation |
| Keyword:
|
finite elements |
| Keyword:
|
convergence |
| Keyword:
|
dual problem |
| Keyword:
|
a posteriori error estimates |
| Keyword:
|
variational inequalities |
| MSC:
|
35J05 |
| MSC:
|
65N15 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0638.65077 |
| idMR:
|
MR0934370 |
| DOI:
|
10.21136/AM.1988.104282 |
| . |
| Date available:
|
2008-05-20T18:33:40Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104282 |
| . |
| Reference:
|
[1] I. Hlaváček: Dual finite element analysis for semi-coercive unilateral boundary value problems.Apl. Mat. 23 (1978), 52-71. MR 0480160 |
| Reference:
|
[2] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary.Apl. Mat. 22 (1977), 244-255. MR 0440958 |
| Reference:
|
[3] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. Mat. 21 (1976), 43-65. MR 0398126 |
| Reference:
|
[4] R. S. Falk: Error estimate for the approximation of a class of variational inequalities.Math. Comp. 28 (1974), 963-971. MR 0391502, 10.1090/S0025-5718-1974-0391502-8 |
| Reference:
|
[5] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I: Primal Theory.Numer. Math. 28 (1977), 431-443. MR 0448949, 10.1007/BF01404345 |
| Reference:
|
[6] J. Haslinger: Finite element analysis for unilateral problem with obstacles on the boundary.Apl. Mat. 22 (1977), 180-188. MR 0440956 |
| Reference:
|
[7] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Apl. Mat. 22 (1977), 14-51. MR 0426453 |
| Reference:
|
[8] I. Hlaváček: Convergence of dual finite element approximations for unilateral boundary value problems.Apl. Mat. 25 (1980), 375-386. MR 0590491 |
| Reference:
|
[9] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892 |
| . |
