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Title: Convergence of dual finite element approximations for unilateral boundary value problems (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 25
Issue: 5
Year: 1980
Pages: 375-386
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: 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. (English)
Keyword: dual finite element approximations
Keyword: unilateral boundary value problems
Keyword: convergence
MSC: 35J05
MSC: 65N30
MSC: 74A55
MSC: 74M15
idZBL: Zbl 0462.65064
idMR: MR0590491
DOI: 10.21136/AM.1980.103872
Date available: 2008-05-20T18:15:10Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Apl. mat. 22 (1977), 14-51. MR 0426453
Reference: [2] I. Hlaváček: Dual finite element analysis for elliptic problems with obstacles on the boundary I.Apl. mat. 22 (1977), 244-255. MR 0440958
Reference: [3] I. Hlaváček: Dual finite element analysis for semi-coercive unilateral boundary value problems.Apl. mat. 23 (1978), 52-71. MR 0480160
Reference: [4] J. Haslinger, and I. Hlaváček: Convergence of a finite element method based on the dual variaional formulation.Apl. mat. 21 (1976), 43 - 65. MR 0398126
Reference: [5] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892
Reference: [6] I. Hlaváček, J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics.Apl. mat. 22 (1.977), 215 - 228. MR 0446014
Reference: [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.
Reference: [8] J. Frehse: Regularity of solutions for problems with thin obstacles.Math. Zeitschrift 143 (1975), 279-288. 10.1007/BF01214380
Reference: [9] P. Grisvard, G. Iooss: Problèmes aux limites unilatéraux dans les domaines non réguliers.Publ. Seminaires Math., Univ. de Rennes, 1976.
Reference: [10] I. Hlaváček: Convergence of an equilibrium finite element model for plane elastostatics.Apl. mat. 24 (1979), 427-457. MR 0547046


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