Geodesic
Dual finite element analysis for an inequality of the 2nd order
Applications of Mathematics, Tome 24 (1979) no. 2, pp. 118-132
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1979.103788
Classification : 35R35, 49J40, 65N30
Keywords: dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations 
@article{10_21136_AM_1979_103788,
     author = {Haslinger, Jaroslav},
     title = {Dual finite element analysis for an inequality of the 2nd order},
     journal = {Applications of Mathematics},
     pages = {118--132},
     year = {1979},
     volume = {24},
     number = {2},
     doi = {10.21136/AM.1979.103788},
     mrnumber = {0523228},
     zbl = {0424.65057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103788/}
}
TY  - JOUR
AU  - Haslinger, Jaroslav
TI  - Dual finite element analysis for an inequality of the 2nd order
JO  - Applications of Mathematics
PY  - 1979
SP  - 118
EP  - 132
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103788/
DO  - 10.21136/AM.1979.103788
LA  - en
ID  - 10_21136_AM_1979_103788
ER  - 
%0 Journal Article
%A Haslinger, Jaroslav
%T Dual finite element analysis for an inequality of the 2nd order
%J Applications of Mathematics
%D 1979
%P 118-132
%V 24
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1979.103788/
%R 10.21136/AM.1979.103788
%G en
%F 10_21136_AM_1979_103788
Haslinger, Jaroslav. Dual finite element analysis for an inequality of the 2nd order. Applications of Mathematics, Tome 24 (1979) no. 2, pp. 118-132. doi: 10.21136/AM.1979.103788

[1] I. Babuška: Approximation by hill-functions II. Institute for fluid Dynamics and Applied mathematics. Technical note BN-708. | MR

[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

[3] J. Haslinger I. Hlaváček: Convergence of finite element method based on the dual variational formulation. Apl. Mat. 21 1976, 43 - 65. | MR

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

[5] J. Haslinger: Finite element analysis for unilateral problems with obstacles on the boundary. Apl. Mat. 22 1977, 180-189. | MR | Zbl

[6] J. Haslinger: A note on a dual finite element method. CMUC 17, 4 1976, 665 - 673. | MR | Zbl

[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

[8] J. Cea: Optimisation, théorie et algorithmes. Dunod, Paris 1971. | MR | Zbl

[9] G. Strang: Approximations in the finite element method. Numer. Math. 19, 81 - 98. | DOI | MR

[10] J. L. Lions: Quelques Méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris. | Zbl

[11] P. A. Raviart: Hybrid finite element methods for solving 2nd order elliptic equations. Conference on Numer. Analysis, Dublin, 1974.

[12] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems. Apl. Mat. 22 1977, 14-51. | MR

[13] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary, I. Ap. Mat. 22 (1977), 244-255. | MR

Cité par Sources :