A block monotone domain decomposition algorithm for a semilinear convection--diffusion problem
type: Item
instance of: scholarly article
title: A block monotone domain decomposition algorithm for a semilinear convection--diffusion problem
zbMATH Open document ID: 1067.65142
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: This paper presents a method for computing converging sequences of upper and lower solutions to a semilinear convection-diffusion equation on the unit square. Singular perturbation is handled by the use of a Shishkin mesh. Upwind differencing is used for the convection terms. A domain decomposition into vertical strips is also given, and the resulting discrete problem is solved by a Schwarz alternating method with iterations proceeding in the downwind direction.
reviewed by: Gerald W. Hedstrom
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 2137291
zbMATH Keywords: semilinear convection-diffusion equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: domain decomposition
zbMATH Keywords: monotone iterations
zbMATH Keywords: Shishkin mesh
zbMATH Keywords: Schwarz alternating method
author: Igor Boglaev
MaRDI profile type: Publication
full work available at URL: j.cam.2004.03.011
OpenAlex ID: W2001794739
cites work: Numerical solution of a quasilinear parabolic equation with a boundary layer
cites work: On monotone iterative methods for a nonlinear singularly perturbed reaction--diffusion problem.
cites work: A monotone Schwarz algorithm for a semilinear convection–diffusion problem
cites work: Domain decomposition for an advection--diffusion problem with parabolic layers.
cites work: Q4035860
cites work: A Parallel Schwarz Method for a Convection-Diffusion Problem
cites work: Linear and quasilinear elliptic equations
cites work: Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
cites work: Q4730721
cites work: On linear monotone iteration and Schwarz methods for nonlinear elliptic PDEs
cites work: Q4486278
cites work: Nonlinear elliptic boundary-value problems in unbounded domains
cites work: Block monotone iterative methods for numerical solutions of nonlinear elliptic equations
cites work: A note on the conditioning of upwind schemes on Shishkin meshes
cites work: GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
cites work: Q4528992
cites work: Q5342712
DOI: 10.1016/J.CAM.2004.03.011
description: scientific article; zbMATH DE number 2137291