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., 2009, Volume 49, Number 1,Pages <nobr>152

This article is cited in 3 papers

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

A. A. Kuleshov^a, V. V. Mymrin^a, A. V. Razgulin^b

^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.

UDC: 519.634

Received: 28.04.2008