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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
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
Linking options:
https://www.mathnet.ru/eng/mm1183 https://www.mathnet.ru/eng/mm/v11/i11/p75
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Abstract page: | 355 | Full-text PDF : | 135 | First page: | 1 |
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