# Dual finite element analysis for elliptic problems with obstacles on the boundary. I

Aplikace matematiky (1977)

- Volume: 22, Issue: 4, page 244-255
- ISSN: 0862-7940

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topHlaváček, Ivan. "Dual finite element analysis for elliptic problems with obstacles on the boundary. I." Aplikace matematiky 22.4 (1977): 244-255. <http://eudml.org/doc/15012>.

@article{Hlaváček1977,

abstract = {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.},

author = {Hlaváček, Ivan},

journal = {Aplikace matematiky},

keywords = {elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds; elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds},

language = {eng},

number = {4},

pages = {244-255},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Dual finite element analysis for elliptic problems with obstacles on the boundary. I},

url = {http://eudml.org/doc/15012},

volume = {22},

year = {1977},

}

TY - JOUR

AU - Hlaváček, Ivan

TI - Dual finite element analysis for elliptic problems with obstacles on the boundary. I

JO - Aplikace matematiky

PY - 1977

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 22

IS - 4

SP - 244

EP - 255

AB - 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.

LA - eng

KW - elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds; elliptic model problem; dual variational formulation; piecewise linear finite elements; a priori error estimates; a posteriori error estimates; two-sided bounds

UR - http://eudml.org/doc/15012

ER -

## References

top- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
- G. N. Jakovlev, Boundary properties of functions of class ${W}_{p}^{\left(1\right)}$ on the domains with angular points, (in Russian). DAN SSSR, 140 (1961), 73-76. (1961) MR0136988
- I. Hlaváček, Dual finite element analysis for unilateral boundary value problems, Aplikace matematiky 22 (1977), 14-51. (1977) Zbl0416.65070MR0426453
- J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892
- U. Mosco G. Strang, 10.1090/S0002-9904-1974-13477-4, Bull. Am. Soc. 80 (1974), 308-312. (1974) Zbl0278.35026MR0331818DOI10.1090/S0002-9904-1974-13477-4
- I. Hlaváček, Some equilibrium and mixed models in the finite element method, Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). Zbl0376.35018MR0514379

## Citations in EuDML Documents

top- Jaroslav Haslinger, Finite element analysis for unilateral problems with obstacles on the boundary
- Ivan Hlaváček, Dual finite element analysis for unilateral boundary value problems
- Ivan Hlaváček, Dual finite element analysis for semi-coercive unilateral boundary value problems
- Jaroslav Haslinger, Dual finite element analysis for an inequality of the 2nd order
- Van Bon Tran, Finite element analysis of primal and dual variational formulations of semicoercive elliptic problems with nonhomogeneous obstacles on the boundary
- Ivan Hlaváček, Convergence of dual finite element approximations for unilateral boundary value problems

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