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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 152–177 (Mi zvmmf59)  

This article is cited in 3 scientific papers (total in 3 papers)

Strong convergence of difference approximations in the problem of transverse vibrations of thin elastic plates

A. A. Kuleshova, V. V. Mymrina, A. V. Razgulinb

a Institute of Mathematical Modeling, Russian Academy of Sciences, pl. Miusskaya 4a, Moscow, 125047, Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: The problem of transverse vibrations of a thin elastic plate is considered. It is proved that the differential operators of the boundary value problem are regularly elliptic, and weak solutions are estimated. For a previously developed difference method, the solution to the difference problem is proved to converge strongly to a weak solution of the original differential problem and the rate of convergence is estimated.

Key words: thin elastic plate, vibration equation, weak solutions, regular ellipticity, estimates of weak solutions, difference method, strong convergence.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 146–171

Bibliographic databases:

UDC: 519.634
Received: 28.04.2008

Citation: A. A. Kuleshov, V. V. Mymrin, A. V. Razgulin, “Strong convergence of difference approximations in the problem of transverse vibrations of thin elastic plates”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 152–177; Comput. Math. Math. Phys., 49:1 (2009), 146–171

Citation in format AMSBIB
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\pages 152--177
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kuleshov A.A., Mymrin V.V., “Modelirovanie kolebanii plavayuschego lda pri posadke samoletov na ledovye aerodromy”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 11:1 (2010), 7–13  mathnet  elib
    2. Kuleshov A.A., “Reduction method with finite-difference approximation for the model of small transverse vibrations in thin elastic”, Latest trends on engineering mechanics, structures, engineering geology, Mathematics and Computers in Science and Engineering, 2010, 44–47  isi
    3. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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