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

Ivan Hlaváček

Aplikace matematiky (1977)

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

Abstract

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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.

How to cite

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Hlaváček, 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

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  1. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  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. (1961) MR0136988
  3. I. Hlaváček, Dual finite element analysis for unilateral boundary value problems, Aplikace matematiky 22 (1977), 14-51. (1977) Zbl0416.65070MR0426453
  4. J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892
  5. 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
  6. 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

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

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