| Title:
|
Dual finite element analysis for an inequality of the 2nd order (English) |
| Author:
|
Haslinger, Jaroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
24 |
| Issue:
|
2 |
| Year:
|
1979 |
| Pages:
|
118-132 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
The dual variational formulation of some free boundary value problem is given and its approximation by finite element method is studied, using piecewise linear elements with non-positive divergence. (English) |
| Keyword:
|
dual variational formulation |
| Keyword:
|
free boundary value problem |
| Keyword:
|
finite element method |
| Keyword:
|
elliptic inequality |
| Keyword:
|
rate of convergence |
| Keyword:
|
Ritz approximations |
| MSC:
|
35R35 |
| MSC:
|
49J40 |
| MSC:
|
65N30 |
| idZBL:
|
Zbl 0424.65057 |
| idMR:
|
MR0523228 |
| DOI:
|
10.21136/AM.1979.103788 |
| . |
| Date available:
|
2008-05-20T18:11:24Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103788 |
| . |
| Reference:
|
[1] I. Babuška: Approximation by hill-functions II.Institute for fluid Dynamics and Applied mathematics. Technical note BN-708. MR 0305550 |
| Reference:
|
[2] F. Brezzi W. W. Hager P. A. Raviart: Error estimates for the finite element solution of variational inequalities. Part I: Primal Theory.(preprint). MR 0448949 |
| Reference:
|
[3] J. Haslinger I. Hlaváček: Convergence of finite element method based on the dual variational formulation.Apl. Mat. 21 1976, 43 - 65. MR 0398126 |
| Reference:
|
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584 |
| Reference:
|
[5] J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary.Apl. Mat. 22 1977, 180-189. Zbl 0434.65083, MR 0440956 |
| Reference:
|
[6] J. Haslinger: A note on a dual finite element method.CMUC 17, 4 1976, 665 - 673. Zbl 0361.65095, MR 0431750 |
| Reference:
|
[7] P. G. Ciarlet P. A. Raviart: General Lagrange and Herniite interpolation in $R^n$ with applications to finite element methods.Arch. Rational Mech. Anal. 46 1972, 217-249. MR 0336957 |
| Reference:
|
[8] J. Cea: Optimisation, théorie et algorithmes.Dunod, Paris 1971. Zbl 0211.17402, MR 0298892 |
| Reference:
|
[9] G. Strang: Approximations in the finite element method.Numer. Math. 19, 81 - 98. MR 0305547, 10.1007/BF01395933 |
| Reference:
|
[10] J. L. Lions: Quelques Méthodes de résolution des problèmes aux limites non linéaires.Dunod, Paris. Zbl 0248.35001 |
| Reference:
|
[11] P. A. Raviart: Hybrid finite element methods for solving 2nd order elliptic equations.Conference on Numer. Analysis, Dublin, 1974. |
| Reference:
|
[12] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Apl. Mat. 22 1977, 14-51. MR 0426453 |
| Reference:
|
[13] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary, I.Ap. Mat. 22 (1977), 244-255. MR 0440958 |
| . |
