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
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.
quasi-linear hyperbolic equation, projection-difference method, asymptotic error estimates.
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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
\paper On error estimates for schemes of the projection-difference method for hyperbolic equations
\jour Sib. Zh. Vychisl. Mat.
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This publication is cited in the following articles:
S. E. Zhelezovsky, “Study of convergence of the projection-difference method for hyperbolic equations”, Siberian Math. J., 48:1 (2007), 76–83
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
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