A finite difference analysis of a streamline diffusion method on a Shishkin mesh
type: Item
instance of: scholarly article
title: A finite difference analysis of a streamline diffusion method on a Shishkin mesh
zbMATH Open document ID: 0916.65108
DOI: 10.1023/A:1019185802623
author: Martin Stynes
author: Lutz Tobiska
published in: Numerical Algorithms
publication date: 1999-07-06T00:00:00Z
review text: The authors consider a singularly perturbed convection-diffusion boundary value problem whose solution has a single boundary layer. They use the streamline diffusion finite element method (SDFEM) to solve the problem. In fact, this SDFEM generates a finite differences scheme which satisfies a discrete maximum principle. This principle is the key fact in order to obtain the sharpest possible results. Moreover, the authors get to a relationship between the error in the numerical solution and a parameter of the Shishkin mesh. Some numerical experiments confirm the theoretical results.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1268413
zbMATH Keywords: finite difference analysis
zbMATH Keywords: singular perturbation
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: error bound
zbMATH Keywords: convection-diffusion boundary value problem
zbMATH Keywords: boundary layer
zbMATH Keywords: streamline diffusion finite element method
zbMATH Keywords: discrete maximum principle
zbMATH Keywords: numerical experiments
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: a:1019185802623
OpenAlex ID: W67803107
description: scientific article; zbMATH DE number 1268413