An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
type: Item
instance of: scholarly article
title: An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
zbMATH Open document ID: 0939.65116
DOI: 10.1016/S0377-0427(99)00198-3
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-12T00:00:00Z
review text: An upwind difference scheme on a novel layer-adapted mesh (a modification of Shishkin piecewise uniform mesh) is considered for a linear singularly perturbed convection-diffusion problem in two dimensions. It is proved that the upwind scheme on the modified Shishkin mesh is first-order convergent in the discrete \(L^\infty\) norm. The new mesh yields more accurate results than simple upwinding on a standard Shishkin mesh, even though it requires essentially the same computational effort. Numerical experiments are presented, which confirm the theoretical results.
reviewed by: Zbigniew Dżygadło
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N50
zbMATH DE Number: 1367869
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical experiments
zbMATH Keywords: convergence
zbMATH Keywords: upwind difference scheme
zbMATH Keywords: convection-diffusion problem
zbMATH Keywords: Shishkin mesh
author: Torsten Linss
MaRDI profile type: Publication
cites work: A study of difference schemes with the first derivative approximated by a central difference ratio
cites work: Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: A hybrid difference scheme on a Shishkin mesh for linear convection-diffusion problems
cites work: Q4865485
cites work: Layer-Adapted Grids for Singular Perturbation Problems
cites work: Q4871736
cites work: Q4697772
full work available at URL: s0377-0427(99)00198-3
OpenAlex ID: W2154622683
description: scientific article; zbMATH DE number 1367869