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Strong-Norm Convergence of the Errors of the Projective-Difference Method with the Crank–Nicolson Scheme in Time for a Parabolic Equation with a Periodic Condition on the Solution

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Abstract

In a separable Hilbert space, a smoothly solvable linear variational parabolic equation with a periodic condition on the solution is solved approximately by the projective-difference method. The discretization of the problem in space is carried out by the Galerkin method, and in time, using the Crank–Nicolson scheme. In this paper, time- and space-efficient estimates are established in strong norms of the errors of approximate solutions. These estimates permit one to obtain the rate of convergence of the error in time to zero up to the second order. In addition, the error estimates take into account the approximation properties of the projection subspaces; this is illustrated using subspaces of the finite element type.

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  1. Voronezh State University, Voronezh, 394018, Russia

    A. S. Bondarev

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  1. A. S. Bondarev
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Correspondence to A. S. Bondarev.

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Translated by V. Potapchouck

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Bondarev, A.S. Strong-Norm Convergence of the Errors of the Projective-Difference Method with the Crank–Nicolson Scheme in Time for a Parabolic Equation with a Periodic Condition on the Solution. Diff Equat 58, 691–697 (2022). https://doi.org/10.1134/S0012266122050081

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  • DOI: https://doi.org/10.1134/S0012266122050081

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