Interaction of boundary layers and corner singularities
type: Item
instance of: scholarly article
title: Interaction of boundary layers and corner singularities
zbMATH Open document ID: 1161.65086
author: C. Jung
author: R. Temam
published in: Discrete and Continuous Dynamical Systems
publication date: 2009-02-19T00:00:00Z
review text: The authors consider a constant coefficient elliptic problem in the unit square, physically a convection-diffusion-reaction problem. They are interested in interaction of the boundary layers due to a small diffusion coefficient with the corner singularities. After analysing the behaviour of the exact solution and its relation to a boundary element with support in only one element, they consider, on an equidistant mesh, a \(Q_1\)-finite element space enriched by this boundary element. They prove that, e.g., \(H_1\) approximation is possible when \(h=o(\varepsilon^{1/2})\), instead of \(h=o(\varepsilon^{3/2})\) in other approaches. A series of numerical experiments verifies this conclusion (for \(\varepsilon\) up to \(10^{-15}\)) and illustrates also that the numerical solution detoriates for small \(\varepsilon\) on a fixed mesh. The case of a diffusion-convection problem is not handled fully in the analysis.
reviewed by: Gisbert Stoyan
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5509438
zbMATH Keywords: convection-diffusion-reaction equation
zbMATH Keywords: constant coefficients
zbMATH Keywords: boundary layers
zbMATH Keywords: corner singularities
zbMATH Keywords: finite elements
zbMATH Keywords: boundary layer element
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: dcds.2009.23.315
OpenAlex ID: W2068526733
DOI: 10.3934/DCDS.2009.23.315
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description: scientific article; zbMATH DE number 5509438