Incremental unknowns for convection-diffusion equations
type: Item
instance of: scholarly article
title: Incremental unknowns for convection-diffusion equations
zbMATH Open document ID: 0774.65074
DOI: 10.1016/0168-9274(93)90060-5
author: Min Chen
author: R. Temam
published in: Applied Numerical Mathematics
publication date: 1993-05-16T00:00:00Z
review text: The authors employ the method of incremental unknowns as suggested by the second author [SIAM J. Math. Anal. 21, No. 1, 154-178 (1990; Zbl 0715.35039)] to improve the convergence rate for some iterative methods applied to finite difference schemes for convection-diffusion equations. It is shown theoretically that, by use of incremental unknowns, condition numbers \((\nu(A)=\lambda_{\max}(A^ t A)^{1/2})/\lambda_{\min}(A+A^ t)\) with \(A+A^ t\) positive) are improved from \(O(h^{-2})\) to \(O((\log h)^ 2)\), when the mesh size \(h\to 0\). Convergence rates are also estimated -- by theoretical methods as well as by numerical tests.
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 166548
zbMATH Keywords: method of incremental unknowns
zbMATH Keywords: convergence rate
zbMATH Keywords: iterative methods
zbMATH Keywords: finite difference schemes
zbMATH Keywords: convection-diffusion equations
zbMATH Keywords: condition numbers
zbMATH Keywords: numerical tests
reviewed by: S. Leif Svensson
MaRDI profile type: Publication
full work available at URL: 0168-9274(93)90060-5
OpenAlex ID: W1973053817
cites work: Incremental unknowns for solving partial differential equations
cites work: Incremental Unknowns in Finite Differences: Condition Number of the Matrix
cites work: Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
cites work: Q3359644
cites work: Inertial Manifolds and Multigrid Methods
description: scientific article; zbMATH DE number 166548