Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations
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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 wordsparabolic equation Hilbert space approximate solution discretization Galerkin's method Euler's implicit method coercive error estimate
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- 1.J.-L. Lions and E. Magenes,Problèmes aux limites non-homogènes et applications, Dunod, Paris (1969).Google Scholar
- 2.Yu. M. Berezanskii,Expansion in the Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).Google Scholar
- 3.Functional Analysis (S. G. Krein, editor) [in Russian], Nauka, Moscow (1972).Google Scholar
- 8.G. I. Marchuk and V. I. Agoshkov,Introduction to Projective-Difference Methods [in Russian], Nauka, Moscow (1981).Google Scholar
- 10.G. Strang and G. Fix,An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs (USA) (1973).Google Scholar