A. A. Samarskii, P. N. Vabishchevich, A. N. Zyl, P. P. Matus, “Difference scheme of the second order of accuracy for dirichlet problem in arbitrary area”, Matem. Mod., 11:9 (1999), 71

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Matematicheskoe modelirovanie, 1999, Volume 11, Number 9, Pages 71–82 (Mi mm1162)

This article is cited in 1 scientific paper (total in 1 paper)

Computational methods and algorithms

Difference scheme of the second order of accuracy for dirichlet problem in arbitrary area

A. A. Samarskii^a, P. N. Vabishchevich^a, A. N. Zyl^b, P. P. Matus^b

^a Institute for Mathematical Modelling, Russian Academy of Sciences
^b Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

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Abstract: Difference schemes for two-dimensional Poisson equation in arbitrary domain on standard templates are considered. Tbese schemes also have the second order of local approximation in the nodes near the boundary. The monotonicity of these schemes are proved for a wide class of areas by means of a principle of maximum. Stability of the schemes is proved in the grid norm $W_2^1$ in arbitrary computational domain by the method of energy inequalities.

Received: 12.01.1999

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Language: Russian

Citation: A. A. Samarskii, P. N. Vabishchevich, A. N. Zyl, P. P. Matus, “Difference scheme of the second order of accuracy for dirichlet problem in arbitrary area”, Matem. Mod., 11:9 (1999), 71–82

Citation in format AMSBIB

\Bibitem{SamVabZyl99}

\by A.~A.~Samarskii, P.~N.~Vabishchevich, A.~N.~Zyl, P.~P.~Matus

\paper Difference scheme of the second order of accuracy for dirichlet problem in arbitrary area

\jour Matem. Mod.

\yr 1999

\vol 11

\issue 9

\pages 71--82

\mathnet{http://mi.mathnet.ru/mm1162}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1739085}

\zmath{https://zbmath.org/?q=an:1063.65575}

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https://www.mathnet.ru/eng/mm/v11/i9/p71

This publication is cited in the following 1 articles:

Citing articles in Google Scholar: Russian citations, English citations
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