Regularity and derivative bounds for a convection-diffusion problem with Neumann boundary conditions on characteristic boundaries
type: Item
instance of: scholarly article
title: Regularity and derivative bounds for a convection-diffusion problem with Neumann boundary conditions on characteristic boundaries
zbMATH Open document ID: 1194.35038
DOI: 10.4171/ZAA/1404
author: Aidan Naughton
author: Martin Stynes
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2010-04-01T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: A convection-diffusion problem is considered on the unit square, with convection parallel to two of the square's sides. Dirichlet conditions are imposed on the inflow and outflow boundaries, with Neumann conditions on the other two sides. No assumption is made regarding the corner compatibility of the data. The regularity of the solution is expressed precisely in terms of the regularity and compatibility of the data. Pointwise bounds on all derivatives of the solution are derived and their dependence on the data regularity, its corner compatibility, and on the small diffusion parameter is made explicit. These results extend previous bounds of \textit{C. Jung} and \textit{R. Temam} [Int. J. Numer. Anal. Model. 2, No.~4, 367--408 (2005; Zbl 1103.65115)] and of \textit{C. Clavero, J. L. Gracia, F. Lisbona} and \textit{G. I. Shishkin} [ZAMM, Z. Angew. Math. Mech. 82, No.~9, 631--647 (2002; Zbl 1012.65104)].
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35E20
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 5689268
zbMATH Keywords: characteristic boundary layer
zbMATH Keywords: unit square
zbMATH Keywords: Dirichlet conditions
zbMATH Keywords: Neumann conditions
zbMATH Keywords: corner compatibility
MaRDI profile type: Publication
cites work: A Robust Method of Improved Order for Convection-Diffusion Problems in a Domain with Characteristic Boundaries
cites work: Uniform A Priori Estimates for Singularly Perturbed Elliptic Equations in Multidimensions
cites work: Elliptic partial differential equations of second order
cites work: Q3470840
cites work: Q5487623
cites work: Corner singularities and boundary layers in a simple convection-diffusion problem
cites work: Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem
cites work: Linear and quasilinear elliptic equations
cites work: Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion problem
cites work: Regularity and derivative bounds for a convection-diffusion problem with a Neumann outflow condition
cites work: A technique to prove parameter-uniform convergence for a singularly perturbed convection-diffusion equation
cites work: Q5317949
OpenAlex ID: W2032609684
description: scientific article; zbMATH DE number 5689268