Geodesic
Dual finite element analysis for elliptic problems with obstacles on the boundary. I
Applications of Mathematics, Tome 22 (1977) no. 4, pp. 244-255
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1977.103701
Classification : 35J25, 65K10, 65N15, 65N30
Keywords: elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds 
@article{10_21136_AM_1977_103701,
     author = {Hlav\'a\v{c}ek, Ivan},
     title = {Dual finite element analysis for elliptic problems with obstacles on the boundary. {I}},
     journal = {Applications of Mathematics},
     pages = {244--255},
     year = {1977},
     volume = {22},
     number = {4},
     doi = {10.21136/AM.1977.103701},
     mrnumber = {0440958},
     zbl = {0422.65065},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103701/}
}
TY  - JOUR
AU  - Hlaváček, Ivan
TI  - Dual finite element analysis for elliptic problems with obstacles on the boundary. I
JO  - Applications of Mathematics
PY  - 1977
SP  - 244
EP  - 255
VL  - 22
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103701/
DO  - 10.21136/AM.1977.103701
LA  - en
ID  - 10_21136_AM_1977_103701
ER  - 
%0 Journal Article
%A Hlaváček, Ivan
%T Dual finite element analysis for elliptic problems with obstacles on the boundary. I
%J Applications of Mathematics
%D 1977
%P 244-255
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1977.103701/
%R 10.21136/AM.1977.103701
%G en
%F 10_21136_AM_1977_103701
Hlaváček, Ivan. Dual finite element analysis for elliptic problems with obstacles on the boundary. I. Applications of Mathematics, Tome 22 (1977) no. 4, pp. 244-255. doi: 10.21136/AM.1977.103701

[1] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. | MR

[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

[3] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Aplikace matematiky 22 (1977), 14-51. | MR

[4] J. Céa: Optimisation, théorie et algorithmes. Dunod, Paris 1971. | MR

[5] U. Mosco G. Strang: One-sided approximations and variational inequalities. Bull. Am. Soc. 80 (1974), 308-312. | DOI | MR

[6] I. Hlaváček: Some equilibrium and mixed models in the finite element method. Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). | MR

Cité par Sources :