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Convergence of the Galyorkin method of approximate solving parabolic equation with weight integral condition

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Abstract

In a Hilbert space an abstract linear parabolic equation with a nonlocal weight integral condition is resolved approximatelymaking use of theGalyorkinmethod. Assumptions on projection subspaces are oriented on a usage of finite element method. We consider the case of projection subspaces built by the uniform partition of domain as well as the case of arbitrary projection subspaces. We obtain the errors estimations for approximate solutions and establish estimates of the convergence rate, exact by the order.

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Authors and Affiliations

  1. Voronezh State University, Universitetskaya pl. 1, Voronezh, 394006, Russia

    A. A. Petrova & V. V. Smagin

Authors
  1. A. A. Petrova
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  2. V. V. Smagin
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Correspondence to A. A. Petrova.

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Original Russian Text © A.A. Petrova, V.V. Smagin, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 8, pp. 49–59.

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Petrova, A.A., Smagin, V.V. Convergence of the Galyorkin method of approximate solving parabolic equation with weight integral condition. Russ Math. 60, 42–51 (2016). https://doi.org/10.3103/S1066369X16080053

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  • DOI: https://doi.org/10.3103/S1066369X16080053

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