Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers
type: Item
instance of: scholarly article
title: Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers
zbMATH Open document ID: 0870.65091
author: Martin Stynes
author: Hans-G. Roos
published in: Applications of Mathematics
publication date: 1997-08-07T00:00:00Z
full work available at URL: https://eudml.org/doc/32950
review text: The authors derive necessary conditions for uniform convergence of the finite difference method for solving elliptic boundary value problems with a small diffusion term of the unit square. It is known that these problems have hyperbolic character, which is the main source of numerical difficulties. Exponential and parabolic layers are investigated. The authors prove the non-existence of a five-point scheme, which would be uniformly convergent with respect to the perturbation parameter \(\epsilon \) and discretization parameter \(h.\) They also present necessary conditions for coefficients of a nine-point scheme to ensure uniform convergence.
reviewed by: Michal Křížek
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 1046549
zbMATH Keywords: numerical analysis
zbMATH Keywords: convection-diffusion problems
zbMATH Keywords: boundary layers
zbMATH Keywords: uniform convergence
MaRDI profile type: Publication
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OpenAlex ID: W2736075615
DOI: 10.21136/AM.1996.134326
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description: scientific article; zbMATH DE number 1046549