Fourier analysis of a robust multigrid method for convection-diffusion equations
type: Item
instance of: scholarly article
title: Fourier analysis of a robust multigrid method for convection-diffusion equations
zbMATH Open document ID: 0833.65130
author: Arnold Reusken
published in: Numerische Mathematik
publication date: 1996-03-14T00:00:00Z
review text: The author considers a two-dimensional convection-diffusion problem with constant coefficients and periodic boundary conditions. A particular two- grid method based on a finite difference approach and on an approximation of the Schur complement is presented. As a preconditioner the exact Schur complement of modified fine grid equations is used. By standard Fourier analysis numerous expressions for the eigenvalues of the Schur complement and of the preconditioner are proved. The main result consists in a theorem which establishes an upper bound for the spectral radius of the two-grid iteration matrix that is smaller than one and independent of the mesh size, the convection-diffusion ratio and the flow direction. Numerical results are also presented.
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 802475
zbMATH Keywords: robust multigrid method
zbMATH Keywords: numerical results
zbMATH Keywords: convection-diffusion problem
zbMATH Keywords: two-grid method
zbMATH Keywords: finite difference
zbMATH Keywords: Schur complement
zbMATH Keywords: preconditioner
zbMATH Keywords: Fourier analysis
zbMATH Keywords: spectral radius
reviewed by: Snezhana Gocheva-Ilieva
MaRDI profile type: Publication
full work available at URL: s002110050150
OpenAlex ID: W2032641095
DOI: 10.1007/S002110050150
description: scientific article; zbMATH DE number 802475