This article is cited in 1 scientific paper (total in 1 paper)
Study of convergence of the projection-difference method for hyperbolic equations
S. E. Zhelezovsky
Saratov State Socio-Economic University
We consider the Cauchy problem for an abstract quasilinear hyperbolic equation with variable operator coefficients and a nonsmooth but Bochner integrable free term in a Hilbert space. Under study is the scheme for approximate solution of this problem which is a combination of the Galerkin scheme in space variables and the three-layer difference scheme with time weights. We establish an a priori energy error estimate without any special conditions on the projection subspaces. We give a concrete form of this estimate in the case when discretization in the space variables is carried out by the finite element method (for a partial differential equation) and by the Galerkin method in Mikhlin form.
abstract hyperbolic equation, projection-difference method, Galerkin method, three-layer difference scheme, error estimate.
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Siberian Mathematical Journal, 2007, 48:1, 76–83
S. E. Zhelezovsky, “Study of convergence of the projection-difference method for hyperbolic equations”, Sibirsk. Mat. Zh., 48:1 (2007), 93–102; Siberian Math. J., 48:1 (2007), 76–83
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\paper Study of convergence of the projection-difference method for hyperbolic equations
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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Gavrilov V.S., “Existence and Uniqueness of Solutions of Hyperbolic Equations in Divergence Form With Various Boundary Conditions on Various Parts of the Boundary”, Differ. Equ., 52:8 (2016), 1011–1022
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