Convergence of dual finite element approximations for unilateral boundary value problems

Ivan Hlaváček

Aplikace matematiky (1980)

  • Volume: 25, Issue: 5, page 375-386
  • ISSN: 0862-7940

Abstract

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A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the L 2 -convergence is proved.

How to cite

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Hlaváček, Ivan. "Convergence of dual finite element approximations for unilateral boundary value problems." Aplikace matematiky 25.5 (1980): 375-386. <http://eudml.org/doc/15161>.

@article{Hlaváček1980,
abstract = {A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the $L^2$-convergence is proved.},
author = {Hlaváček, Ivan},
journal = {Aplikace matematiky},
keywords = {dual finite element approximations; unilateral boundary value problems; convergence; dual finite element approximations; unilateral boundary value problems; convergence},
language = {eng},
number = {5},
pages = {375-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of dual finite element approximations for unilateral boundary value problems},
url = {http://eudml.org/doc/15161},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Hlaváček, Ivan
TI - Convergence of dual finite element approximations for unilateral boundary value problems
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 5
SP - 375
EP - 386
AB - A semi-coercive problem with unilateral boundary conditions of the Signoriti type in a convex polygonal domain is solved on the basis of a dual variational approach. Whereas some strong regularity of the solution has been assumed in the previous author’s results on error estimates, no assumption of this kind is imposed here and still the $L^2$-convergence is proved.
LA - eng
KW - dual finite element approximations; unilateral boundary value problems; convergence; dual finite element approximations; unilateral boundary value problems; convergence
UR - http://eudml.org/doc/15161
ER -

References

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  1. I. Hlaváček, Dual finite element analysis for unilateral boundary value problems, Apl. mat. 22 (1977), 14-51. (1977) MR0426453
  2. I. Hlaváček, Dual finite element analysis for elliptic problems with obstacles on the boundary I, Apl. mat. 22 (1977), 244-255. (1977) MR0440958
  3. I. Hlaváček, Dual finite element analysis for semi-coercive unilateral boundary value problems, Apl. mat. 23 (1978), 52-71. (1978) MR0480160
  4. J. Haslinger, and I. Hlaváček, Convergence of a finite element method based on the dual variaional formulation, Apl. mat. 21 (1976), 43 - 65. (1976) MR0398126
  5. J. Céa, Optimisation, théorie et algorithmes, Dunod, Paris 1971. (1971) MR0298892
  6. I. Hlaváček, J. Lovíšek, A finite element analysis for the Signorini problem in plane elastostatics, Apl. mat. 22 (1.977), 215 - 228. MR0446014
  7. G. Fichera, Boundary value problems of elasticity with unilateral constraints, Encycl. of Physics (ed. by S. Fliigge), vol. VIa/2, Springer- Verlag, Berlin, 1972. (1972) 
  8. J. Frehse, 10.1007/BF01214380, Math. Zeitschrift 143 (1975), 279-288. (1975) DOI10.1007/BF01214380
  9. P. Grisvard, G. Iooss, Problèmes aux limites unilatéraux dans les domaines non réguliers, Publ. Seminaires Math., Univ. de Rennes, 1976. (1976) 
  10. I. Hlaváček, Convergence of an equilibrium finite element model for plane elastostatics, Apl. mat. 24 (1979), 427-457. (1979) MR0547046

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