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 Mat. Zametki, 1997, Volume 62, Issue 6, Pages 898–909 (Mi mz1679)

Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations

V. V. Smagin

Voronezh State University

Abstract: Solutions continuously differentiable with respect to time of parabolic equations in Hilbert space are obtained by the projective-difference method approximately. The discretization of the problem is carried out in the spatial variables using Galerkin's method, and in the time variable using Euler's implicit method. Strong-norm error estimates for approximate solutions are obtained. These estimates not only allow one to establish the convergence of the approximate solutions to the exact ones but also yield numerical characteristics of the rates of convergence. In particular, order-sharp error estimates for finite element subspaces are obtained.

DOI: https://doi.org/10.4213/mzm1679

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English version:
Mathematical Notes, 1997, 62:6, 752–761

Bibliographic databases:

UDC: 517.988.8
Revised: 16.06.1997

Citation: V. V. Smagin, “Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations”, Mat. Zametki, 62:6 (1997), 898–909; Math. Notes, 62:6 (1997), 752–761

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz/v62/i6/p898

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Smagin, VV, “Energy error estimates for the projection-difference method with the Crank-Nicolson scheme for parabolic equations”, Siberian Mathematical Journal, 42:3 (2001), 568
2. S. E. Zhelezovsky, “Estimates for the rate of convergence of the projection-difference method for hyperbolic equations”, Russian Math. (Iz. VUZ), 46:1 (2002), 19–28
3. V. V. Smagin, “Strong-Norm Error Estimates for the Projective-Difference Method for Parabolic Equations with Modified Crank–Nicolson Scheme”, Math. Notes, 74:6 (2003), 864–873
4. V. V. Smagin, “On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations”, Math. Notes, 78:6 (2005), 841–852
5. Vinogradova, PV, “Error estimates for a projection-difference method for a linear differential-operator equation”, Differential Equations, 44:7 (2008), 970
6. Chaikovs'kyi A.V., “Functions of Shift Operator and their Applications to Difference Equations”, Ukr. Math. J., 62:10 (2011), 1635–1648
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