Mathematical Notes

, Volume 62, Issue 6, pp 752–761 | Cite as

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

  • V. V. Smagin
Article
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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.

Key words

parabolic equation Hilbert space approximate solution discretization Galerkin's method Euler's implicit method coercive error estimate 

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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. V. Smagin
    • 1
  1. 1.Voronezh State UniversityVoronezhUSSR

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