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Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 8, Pages 1462–1474 (Mi zvmmf431)  

This article is cited in 5 scientific papers (total in 5 papers)

On the convergence of the Galerkin method for coupled thermoelasticity problems

S. E. Zhelezovsky

Saratov State Socioeconomic University, ul. Radishcheva 89, Saratov, 410003, Russia

Abstract: The Cauchy problem for a system of two operator-differential equations is considered that is an abstract statement of linear coupled thermoelasticity problems. Error estimates in the energy norm for the semidiscrete Galerkin method as applied to the Cauchy problem are established without imposing any special conditions on the projection subspaces. By way of illustration, the error estimates are applied to finite element schemes for solving the coupled problem of plate thermoelasticity considered within the framework of the Kirchhoff linearized theory. The results obtained are also applicable to the case when the projection subspaces in the Galerkin method (for the original abstract problem) are the eigenspaces of operators similar to unbounded self-adjoint positive definite operator coefficients of the original equations.

Key words: Galerkin method, error estimates, operator-differential equations, coupled thermoelasticity problems, finite element method.

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English version:
Computational Mathematics and Mathematical Physics, 2006, 46:8, 1387–1398

Bibliographic databases:

UDC: 519.634
Received: 30.01.2006

Citation: S. E. Zhelezovsky, “On the convergence of the Galerkin method for coupled thermoelasticity problems”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1462–1474; Comput. Math. Math. Phys., 46:8 (2006), 1387–1398

Citation in format AMSBIB
\by S.~E.~Zhelezovsky
\paper On the convergence of the Galerkin method for coupled thermoelasticity problems
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 8
\pages 1462--1474
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 8
\pages 1387--1398

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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. S. E. Zhelezovskii, “Error estimates in the projection-difference method for a hyperbolic-parabolic system of abstract differential equations”, Num. Anal. Appl., 3:3 (2010), 218–230  mathnet  crossref  elib  elib
    2. S. E. Zhelezovskiǐ, “On the smoothness of the solution of an abstract coupled problem of thermoelasticity type”, Comput. Math. Math. Phys., 50:7 (2010), 1178–1194  mathnet  crossref  mathscinet  adsnasa  isi
    3. S. E. Zhelezovskii, “The convergence rate of a projection-difference method for an abstract coupled problem”, Russian Math. (Iz. VUZ), 55:9 (2011), 43–51  mathnet  crossref  mathscinet
    4. S. E. Zhelezovskii, “Stability of an operator-difference scheme for thermoelasticity problems”, Russian Math. (Iz. VUZ), 56:6 (2012), 11–19  mathnet  crossref  mathscinet
    5. Zhelezovskii S.E., “Error Estimate for a Symmetric Scheme of the Projection-Difference Method for an Abstract Hyperbolic-Parabolic System of the Type of Systems of Thermoelasticity Equations”, Differ. Equ., 48:7 (2012), 950–964  crossref  mathscinet  zmath  isi  elib  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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