Literature cited
S. A. Voitsekhovskii, V. L. Makarov, A. A. Samarskii, and T. G. Shablii, “On convergence rate estimate for difference solutions to generalized solution of Dirichlet problem for Helmholtz equations in convex polygon,” Dokl. Akad. Nauk SSSR,273, No. 5, 1040–1044 (1983).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press (1968).
I. Nechas, “On solution of second-order partial elliptic differential equations with unbounded Dirichlet integral,” Chekhosl. Mat. Zh.,10, No. 2, 283–298 (1960).
L. A. Oganesyan and L. A. Rukhovets, Variational Difference Methods for Solving Elliptic Equations [in Russian], Izd. Akad. Nauk ArmSSR, Erevan (1979).
J. H. Bramble, T. Duport, and V. Thomee, “Projection methods for Dirichlet's problem in approximating polygonal domains with boundary value corrections,” Math. Comp.,27, No. 120, 869–879 (1972).
V. L. Makarov and A. A. Samarskii, “Application of exact difference schemes to estimating convergence rate of method of straight lines,” Zh. Vychisl. Mat. Mat., Fiz.,20, No. 2, 381–397 (1980).
M. Dryya, “A priori estimates in W2 2 in convex domain for systems of elliptic difference equations,” ibid.,12, No. 6, 1595–1601 (1972).
J. H. Bramble and S. R. Hilbert, “Bounds for a class of linear functionals with applications to Hermite interpolation,” Numer. Math.,16, No. 4, 362–369 (1971).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 38, No. 1, pp. 98–101, January–February, 1986.
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Voitsekhovskii, S.A., Marakov, V.L. & Shablii, T.G. Estimation of convergence rate of different solutions to generalized solution of dirichlet problem for helmholtz equation of class\(\mathop W\limits^0 \) 2 1(Ω) in convex domain. Ukr Math J 38, 88–90 (1986). https://doi.org/10.1007/BF01056766
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DOI: https://doi.org/10.1007/BF01056766