Abstract
Convergence of the approximate solution is proved. Numerical solutions of some examples are given.
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References
I. I. Lyashko, V. V. Skopetskii, and V. S. Deineka, "Numerical discretization of a parabolic equation with discontinuous solution," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 5, 20–24 (1987).
V. V. Stepanov, A Course of Differential Equations [in Russian], Moscow (1968).
J. J. Douglas and T. Dupont, "Galerkin methods for parabolic equations," SIAM J. Num. Anal.,7, No. 4, 575–626 (1970).
Additional information
Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 77–85, 1989.
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Skopetskii, V.V., Deineka, V.S. & Artemenko, A.L. Finite-element discretization of a parabolic equation with a discontinuous solution. J Math Sci 69, 1430–1436 (1994). https://doi.org/10.1007/BF01250587
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DOI: https://doi.org/10.1007/BF01250587