Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh
type: Item
instance of: scholarly article
title: Pointwise convergence of approximations to a convection-diffusion equation on a Shishkin mesh
zbMATH Open document ID: 0942.65090
DOI: 10.1016/S0168-9274(99)00009-4
published in: Applied Numerical Mathematics
publication date: 2000-08-24T00:00:00Z
review text: This paper deals with a singularly perturbed one-dimensional boundary value problem. A standard, centered difference or finite element method on a piecewise equidistant mesh is considered. The author transforms the obtained equations so that the new equations have a monotonicity property and proves pointwise convergence, uniform in the perturbation parameter \(\varepsilon\) of second-order with respect to the number of nodes \(N\) on the coarse mesh, while the convergence is of order \(O(N^{-2}\ln^2 N)\) on the fine mesh. Some numerical results are presented.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 1399550
zbMATH Keywords: convection-diffusion equation
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: finite difference method
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary value problem
zbMATH Keywords: finite element method
zbMATH Keywords: convergence
zbMATH Keywords: numerical results
author: Wim Lenferink
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: s0168-9274(99)00009-4
OpenAlex ID: W2016471032
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description: scientific article; zbMATH DE number 1399550