Abstract
We establish the convergence of the Rothe method for a parabolic equation with nonlocal boundary conditions and obtain an a priori estimate for the constructed difference scheme in the grid norm on a ball. We prove that the suggested iterative process for the solution of the posed problem converges in the small.
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 244–254, February, 1997.
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Mitropol’skii, Y.A., Berezovskii, A.A. & Shkhanukov-Lafishev, M.K. Nonlinear nonlocal problems for a parabolic equation in a two-dimensional domain. Ukr Math J 49, 269–280 (1997). https://doi.org/10.1007/BF02486441
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DOI: https://doi.org/10.1007/BF02486441