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This article is cited in 2 scientific papers (total in 2 papers)
Study of convergence of the projection-difference method for hyperbolic equations
S. E. Zhelezovsky Saratov State Socio-Economic University
Abstract:
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.
Keywords:
abstract hyperbolic equation, projection-difference method, Galerkin method, three-layer difference scheme, error estimate.
Received: 15.06.2005 Revised: 15.03.2006
Citation:
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
Linking options:
https://www.mathnet.ru/eng/smj9 https://www.mathnet.ru/eng/smj/v48/i1/p93
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Abstract page: | 421 | Full-text PDF : | 106 | References: | 69 |
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