This article is cited in 11 scientific papers (total in 11 papers)
Grid approximation of a singularly perturbed elliptic equation with convective terms in the presence of various boundary layers
G. I. Shishkin
Institute of Mathematics and Mechanics, Ural Division, Russian Academy of Sciences, ul. S. Kovalevskoi 16, Yekaterinburg, 620219, Russia
The Dirichlet problem for a singularly perturbed elliptic convection-diffusion equation in a rectangle and in a vertical half-strip with a vector perturbation parameter $\varepsilon=(\varepsilon_1,\varepsilon_2)$ is considered. The higher derivatives of the equation and the first derivative with respect to the vertical coordinate include the parameters $\varepsilon_1$ and $\varepsilon_2$, respectively, which can take arbitrary values in the intervals $(0,1]$ and $[–1,1]$. For small values of $\varepsilon_1$, boundary layers appear in the neighborhood of various parts of the domain boundary. The type of these layers depends on the relation between $\varepsilon_1$ and $\varepsilon_2$: they can be regular, parabolic, or hyperbolic. Their characteristics also depend on the relation between $\varepsilon_1$ and $\varepsilon_2$. Using the special grid technique (these grids are condensing in the boundary layers), finite difference schemes are constructed that $\varepsilon$-uniformly converge in the maximum norm.
singularly perturbed problem for the elliptic equation, grid approximation, convergence, special grids.
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Computational Mathematics and Mathematical Physics, 2005, 45:1, 104–119
G. I. Shishkin, “Grid approximation of a singularly perturbed elliptic equation with convective terms in the presence of various boundary layers”, Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005), 110–125; Comput. Math. Math. Phys., 45:1 (2005), 104–119
Citation in format AMSBIB
\paper Grid approximation of a singularly perturbed elliptic equation with convective terms in the presence of various boundary layers
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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