
This article is cited in 2 scientific papers (total in 2 papers)
Grid approximations of singularly perturbed systems for parabolic convectiondiffusion equations with counterflow
G. I. Shishkin^{} ^{} Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Abstract:
The first boundary value problem is considered on a strip for a system of two singularly perturbed parabolic
equations. The perturbation parameters multiplying the highest derivatives of each of the equations are
mutually independent and can take arbitrary values from the interval $(0,1]$. When these parameters equal
zero, the system of parabolic equations degenerates into a system of hyperbolic first order equations coupled
by the reaction terms. The convective terms (i.e., their components orthogonal to the boundaries of the strip)
that are involved in the different equations have the opposite directions (convection with counterflow). This
case brings us to the appearance of boundary layers in the neighbourhood of both boundaries of the strip. For
this boundary value problem, the difference schemes that converge uniformly with respect to the parameters
are constructed here using the condensing mesh method. We also consider the construction of parameter
uniform convergent difference schemes for a system of singularly perturbed elliptic equations that degenerate
into first order equations if the parameter equals zero.
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519.632/633 Received: 10.12.1997
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Citation:
G. I. Shishkin, “Grid approximations of singularly perturbed systems for parabolic convectiondiffusion equations with counterflow”, Sib. Zh. Vychisl. Mat., 1:3 (1998), 281–297
Citation in format AMSBIB
\Bibitem{Shi98}
\by G.~I.~Shishkin
\paper Grid approximations of singularly perturbed systems for parabolic convectiondiffusion equations with counterflow
\jour Sib. Zh. Vychisl. Mat.
\yr 1998
\vol 1
\issue 3
\pages 281297
\mathnet{http://mi.mathnet.ru/sjvm309}
\mathscinet{http://www.ams.org/mathscinetgetitem?mr=1699491}
\zmath{https://zbmath.org/?q=an:0917.65079}
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This publication is cited in the following articles:

Kopteva N., O'Riordan E., “Shishkin Meshes in the Numerical Solution of Singularly Perturbed Differential Equations”, Int J Numer Anal Model, 7:3 (2010), 393–415

Roos H.G., Schopf M., “Layer Structure and the Galerkin Finite Element Method For a System of Weakly Coupled Singularly Perturbed ConvectionDiffusion Equations With Multiple Scales”, ESAIMMath. Model. Numer. Anal.Model. Math. Anal. Numer., 49:5 (2015), 1525–1547

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