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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 4, Pages 727–754 (Mi zvmmf491)  

Finite-difference scheme for two-scale homogenized equations of one-dimensional motion of a thermoviscoelastic Voigt-type body

A. A. Amosov, A. E. Vestfal'skii

Department of Mathematical Modeling, Moscow Power Engineering Institute (Technical University), ul. Krasnokazarmennaya 14, Moscow, 111250, Russia

Abstract: The Bakhvalov–Eglit two-scale homogenized equations are used to describe the motion of layered periodic compressible media with rapidly oscillating data. A new finite-difference scheme for a system of such equations is proposed and analyzed in the case of a thermoviscoelastic Voigt-type body. A priori estimates of solutions are derived for nonsmooth data. The existence and uniqueness of discrete solutions are established. A theorem is proved on the convergence of a subsequence of discrete solutions to a weak solution of the problem under study. Simultaneously, a new theorem on the existence of global weak solutions is deduced.

Key words: finite-difference scheme, two-scale homogenized equations, thermoviscoelastic Voigt-type body, global weak solution.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:4, 691–718

Bibliographic databases:

UDC: 519.934
Received: 11.11.2005

Citation: A. A. Amosov, A. E. Vestfal'skii, “Finite-difference scheme for two-scale homogenized equations of one-dimensional motion of a thermoviscoelastic Voigt-type body”, Zh. Vychisl. Mat. Mat. Fiz., 46:4 (2006), 727–754; Comput. Math. Math. Phys., 46:4 (2006), 691–718

Citation in format AMSBIB
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\by A.~A.~Amosov, A.~E.~Vestfal'skii
\paper Finite-difference scheme for two-scale homogenized equations of one-dimensional motion of a~thermoviscoelastic Voigt-type body
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 4
\pages 727--754
\mathnet{http://mi.mathnet.ru/zvmmf491}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2260360}
\zmath{https://zbmath.org/?q=an:05200939}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 4
\pages 691--718
\crossref{https://doi.org/10.1134/S0965542506040142}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746062772}


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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