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Title: The density of solenoidal functions and the convergence of a dual finite element method (English)
Author: Hlaváček, Ivan
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 25
Issue: 1
Year: 1980
Pages: 39-55
Summary lang: English
Summary lang: Czech
Summary lang: Russian
Category: math
Summary: A proof is given of the following theorem: infinitely differentiable solenoidal vector - functions are dense in the space of functions, which are solenoidal in the distribution sense only. The theorem is utilized in proving the convergence of a dual finite element procedure for Dirichlet, Neumann and a mixed boundary value problem of a second order elliptic equation. (English)
Keyword: density of solenoidal functions
Keyword: convergence of a dual finite element method
Keyword: Dirichlet, Neumann and a mixed boundary value problem
Keyword: second order elliptic equation
MSC: 35J25
MSC: 46E35
MSC: 65N30
idZBL: Zbl 0424.65056
idMR: MR0554090
DOI: 10.21136/AM.1980.103836
Date available: 2008-05-20T18:13:34Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] J. Haslinger I. Hlaváček: Convergence of a finite element method based on the dual variational formulation.Apl. mat. 21 (1976), 43 - 65. MR 0398126
Reference: [2] B. Fraeijs de Veubeke M. Hogge: Dual analysis for heat conduction problems by finite elements.Int. J. Numer. Meth. Eng. 5 (1972), 65 - 82. 10.1002/nme.1620050107
Reference: [3] J. Nečas: Les méthodes directes en théorie des équations elliptiques.Academia, Prague 1967. MR 0227584
Reference: [4] O. A. Ladyzenskaya: The mathematical theory of viscous incompressible flow.Gordon & Breach, New York 1969. MR 0254401


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