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Sib. Zh. Vychisl. Mat., 2004, Volume 7, Number 4, Pages 309–325 (Mi sjvm167)  

This article is cited in 2 scientific papers (total in 2 papers)

On error estimates for schemes of the projection-difference method for hyperbolic equations

S. E. Zhelezovsky

Saratov State Socio-Economic University

Abstract: We study the convergence of a three-level scheme of the projection-difference method for an abstract quasi-linear hyperbolic equation. We establish asymptotic energy estimates for the error. The order of these estimates is unimprovable. A preliminary result on the conditional stability of the scheme ($W$-stability in the sense of the definition formulated in the paper) forms the basis of our derivation of the estimates. We illustrate the use of our general results by an example of a scheme with finite element space discretization applied to the first initial boundary-value problem for a second-order hyperbolic equation. We also note the possibility of application of our general results in the case when the space discretization is realized by the Galerkin method in the form of Mikhlin.

Key words: quasi-linear hyperbolic equation, projection-difference method, asymptotic error estimates.

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Bibliographic databases:
UDC: 517.988.8+519.633.6
Received: 26.05.2003

Citation: S. E. Zhelezovsky, “On error estimates for schemes of the projection-difference method for hyperbolic equations”, Sib. Zh. Vychisl. Mat., 7:4 (2004), 309–325

Citation in format AMSBIB
\Bibitem{Zhe04}
\by S.~E.~Zhelezovsky
\paper On error estimates for schemes of the projection-difference method for hyperbolic equations
\jour Sib. Zh. Vychisl. Mat.
\yr 2004
\vol 7
\issue 4
\pages 309--325
\mathnet{http://mi.mathnet.ru/sjvm167}
\zmath{https://zbmath.org/?q=an:1068.65114}


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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. Zhelezovsky, “Study of convergence of the projection-difference method for hyperbolic equations”, Siberian Math. J., 48:1 (2007), 76–83  mathnet  crossref  mathscinet  zmath  isi
    2. S. E. Zhelezovsky, “Error estimate in the projection-difference method for an abstract quasilinear hyperbolic equation with a non-smooth right-hand side”, Num. Anal. Appl., 1:2 (2008), 105–113  mathnet  crossref
  • Sibirskii Zhurnal Vychislitel'noi Matematiki
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