Dual finite element analysis for an inequality of the 2nd order

Jaroslav Haslinger

Aplikace matematiky (1979)

  • Volume: 24, Issue: 2, page 118-132
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Haslinger, Jaroslav. "Dual finite element analysis for an inequality of the 2nd order." Aplikace matematiky 24.2 (1979): 118-132. <http://eudml.org/doc/15087>.

@article{Haslinger1979,
abstract = {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.},
author = {Haslinger, Jaroslav},
journal = {Aplikace matematiky},
keywords = {dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations; dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations},
language = {eng},
number = {2},
pages = {118-132},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Dual finite element analysis for an inequality of the 2nd order},
url = {http://eudml.org/doc/15087},
volume = {24},
year = {1979},
}

TY - JOUR
AU - Haslinger, Jaroslav
TI - Dual finite element analysis for an inequality of the 2nd order
JO - Aplikace matematiky
PY - 1979
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 24
IS - 2
SP - 118
EP - 132
AB - 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.
LA - eng
KW - dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations; dual variational formulation; free boundary value problem; finite element method; elliptic inequality; rate of convergence; Ritz approximations
UR - http://eudml.org/doc/15087
ER -

References

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  1. I. Babuška, Approximation by hill-functions II, Institute for fluid Dynamics and Applied mathematics. Technical note BN-708. MR0305550
  2. F. Brezzi W. W. Hager P. A. Raviart, Error estimates for the finite element solution of variational inequalities. Part I: Primal Theory, (preprint). MR0448949
  3. J. Haslinger I. Hlaváček, Convergence of finite element method based on the dual variational formulation, Apl. Mat. 21 1976, 43 - 65. (1976) MR0398126
  4. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague 1967. (1967) MR0227584
  5. J. Haslinger, Finite element analysis for unilateral problems with obstacles on the boundary, Apl. Mat. 22 1977, 180-189. (1977) Zbl0434.65083MR0440956
  6. J. Haslinger, A note on a dual finite element method, CMUC 17, 4 1976, 665 - 673. (1976) Zbl0361.65095MR0431750
  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. (1972) MR0336957
  8. J. Cea, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) Zbl0211.17402MR0298892
  9. G. Strang, 10.1007/BF01395933, Numer. Math. 19, 81 - 98. MR0305547DOI10.1007/BF01395933
  10. J. L. Lions, Quelques Méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris. Zbl0248.35001
  11. P. A. Raviart, Hybrid finite element methods for solving 2nd order elliptic equations, Conference on Numer. Analysis, Dublin, 1974. (1974) 
  12. I. Hlaváček, Dual finite element analysis for unilateral boundary value problems, Apl. Mat. 22 1977, 14-51. (1977) MR0426453
  13. I. Hlaváček, Dual finite element analysis for elliptic problems with obstacles on the boundary, I, Ap. Mat. 22 (1977), 244-255. (1977) MR0440958

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