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Matematicheskoe modelirovanie, 1999, Volume 11, Number 11, Pages 75–90 (Mi mm1183)  

This article is cited in 4 scientific papers (total in 4 papers)

Computational methods and algorithms

Grid approximation of singularly perturbed boundary value problems in a nonconvex domain with a piecewise smooth boundary

G. I. Shishkin

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract: The Dirichlet problem for an elliptic equation is considered on a $L$-shaped domain formed by rectangles. The highest derivatives of the equation are multiplied by a parameter $\varepsilon$ taking arbitrary values in the half-interval (0,1]. For $\varepsilon= 0$ the elliptic equation degenerates into an equation which contains no derivatives. For the boundary-value problem, using the method on the base of classical finite difference schemes, domain decomposition and additive separation of singularities, we construct iterative and iteration-free difference schemes which do converge $\varepsilon$-uniformly. The $\varepsilon$-uniform approximation for the singular part of the solution of the boundary value problem is attained due to the use of special grids that concentrate in the neighbourhood of the boundary layer.
Received: 05.08.1996
Bibliographic databases:
UDC: 519.632/633
Language: Russian
Citation: G. I. Shishkin, “Grid approximation of singularly perturbed boundary value problems in a nonconvex domain with a piecewise smooth boundary”, Matem. Mod., 11:11 (1999), 75–90
Citation in format AMSBIB
\Bibitem{Shi99}
\by G.~I.~Shishkin
\paper Grid approximation of singularly perturbed boundary value problems in a~nonconvex domain with a~piecewise smooth boundary
\jour Matem. Mod.
\yr 1999
\vol 11
\issue 11
\pages 75--90
\mathnet{http://mi.mathnet.ru/mm1183}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1761699}
\zmath{https://zbmath.org/?q=an:1189.65273}
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  • https://www.mathnet.ru/eng/mm/v11/i11/p75
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математическое моделирование
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