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Title: Solution of the first biharmonic problem by the method of least squares on the boundary (English)
Author: Rektorys, Karel
Author: Zahradník, Václav
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 19
Issue: 2
Year: 1974
Pages: 101-131
Summary lang: English
Summary lang: Czech
Category: math
Summary: Some problems of plane elasticity lead to the solution of biharmonic problem. Many methods have been developped to the solution of this problem (the method of finite differences, the finite element method, classical variational methods, methods based on the theory of functions of a complex variable, etc.). In this paper, the method of least squares on the boundary is presented, having its specific preferences. In the first part, the algorithm of this method and a numerical example are given. This part is mainly intended for "consumers" of mathematics and is written in more detail. In the second part, the proof of convergence of the method is given. This part is mainly intended for mathematicians. Applied to the solution of the biharmonic problem, the method takes an essential use of the form of equation. As to its idea itself, it can be applied - in proper modifications - also to the solution of other problems. ()
MSC: 35B45
MSC: 35J05
MSC: 35J40
idZBL: Zbl 0282.35041
idMR: MR0346312
DOI: 10.21136/AM.1974.103518
Date available: 2008-05-20T17:58:21Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] Nečas J.: Les méthodes dlrectes en théorie des équations elliptiques.Praha, Academia 1967. MR 0227584
Reference: [2] Babuška I., Rektorys K., Vyčichlo F.: Matematická teorie rovinné pružnosti.Praha NČSAV 1955. (Mathematische Elastizitätstheorie der ebenen Probleme. Berlin, Akademie-verlag 1960.) MR 0115343
Reference: [3] Rektorys K.: Variational methods in engineering problems and in those of mathematical physics.(Variační metody v inženýrských problémech a v problémech matematické fyziky.) In Czech: Praha, SNTL 1974. In English: Dordrecht (Holland)-Boston, Reidel Co, to appear in 1976. MR 0487652
Reference: [4] Бондаренко В. А.: Полигармонические полиномы.Ташкент, ФАН 1968. Zbl 1171.62301


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