Mixed formulation of elliptic variational inequalities and its approximation

Jaroslav Haslinger

Aplikace matematiky (1981)

  • Volume: 26, Issue: 6, page 462-475
  • ISSN: 0862-7940

Abstract

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The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian 2 on a certain convex set K x Λ . Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.

How to cite

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Haslinger, Jaroslav. "Mixed formulation of elliptic variational inequalities and its approximation." Aplikace matematiky 26.6 (1981): 462-475. <http://eudml.org/doc/15217>.

@article{Haslinger1981,
abstract = {The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian $\mathcal \{2\}$ on a certain convex set $Kx \ \Lambda $. Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.},
author = {Haslinger, Jaroslav},
journal = {Aplikace matematiky},
keywords = {elliptic variational inequalities; mixed formulation; saddle point problem; elliptic variational inequalities; mixed formulation; saddle point problem},
language = {eng},
number = {6},
pages = {462-475},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mixed formulation of elliptic variational inequalities and its approximation},
url = {http://eudml.org/doc/15217},
volume = {26},
year = {1981},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - Mixed formulation of elliptic variational inequalities and its approximation
JO - Aplikace matematiky
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 26
IS - 6
SP - 462
EP - 475
AB - The approximation of a mixed formulation of elliptic variational inequalities is studied. Mixed formulation is defined as the problem of finding a saddle-point of a properly chosen Lagrangian $\mathcal {2}$ on a certain convex set $Kx \ \Lambda $. Sufficient conditions, guaranteeing the convergence of approximate solutions are studied. Abstract results are applied to concrete examples.
LA - eng
KW - elliptic variational inequalities; mixed formulation; saddle point problem; elliptic variational inequalities; mixed formulation; saddle point problem
UR - http://eudml.org/doc/15217
ER -

References

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  1. F. Brezzi W. W. Hager P. A. Raviart, Error estimates for the finite element solution of variational inequalities, Part II: Mixed methods, Numerische Mathematik, 131, 1978, pp. 1-16. (1978) MR0508584
  2. J. Cea, Optimisation, théorie et algorithmes, Dunod, 1971. (1971) Zbl0211.17402MR0298892
  3. I. Ekeland R. Temam, Analyse convexe et problèmes variationnels, Dunod, 1974, Paris. (1974) MR0463993
  4. R. Glowinski J. L. Lions R. Tremolieres, Analyse numérique des inéquations variationnelles, Vol. I., II. Dunod, 1976, Paris. (1976) 
  5. J. Haslinger I. Hlaváček, Approximation of the Signorini problem with friction by the mixed finite element method, to appear in JMAA. 
  6. J. Haslinger J. Lovíšek, Mixed variational formulation of unilateral problems, CMUC 21, 2 (1980), 231-246. (1980) MR0580680
  7. J. Haslinger M. Tvrdý, Numerical solution of the Signorini problem with friction by FEM, to appear. MR1355659

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