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Title: Dual finite element analysis for elliptic problems with obstacles on the boundary. I (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 22
Issue: 4
Year: 1977
Pages: 244-255
Summary lang: English
Summary lang: Czech
Summary lang: Russian
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Category: math
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Summary: 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. (English)
Keyword: elliptic model problem
Keyword: dual variational formulation
Keyword: piecewise linear finite elements
Keyword: a priori error estimates
Keyword: a posteriori error estimates
Keyword: two-sided bounds
MSC: 35J25
MSC: 65K10
MSC: 65N15
MSC: 65N30
idZBL: Zbl 0422.65065
idMR: MR0440958
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Date available: 2008-05-20T18:07:33Z
Last updated: 2015-07-15
Stable URL: http://hdl.handle.net/10338.dmlcz/103701
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Reference: [1] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584
Reference: [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. MR 0136988
Reference: [3] I. Hlaváček: Dual finite element analysis for unilateral boundary value problems.Aplikace matematiky 22 (1977), 14-51. MR 0426453
Reference: [4] J. Céa: Optimisation, théorie et algorithmes.Dunod, Paris 1971. MR 0298892
Reference: [5] U. Mosco G. Strang: One-sided approximations and variational inequalities.Bull. Am. Soc. 80 (1974), 308-312. MR 0331818, 10.1090/S0002-9904-1974-13477-4
Reference: [6] I. Hlaváček: Some equilibrium and mixed models in the finite element method.Proceedings of the Banach Internat. Math. Center, Warsaw (to appear). MR 0514379
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