Multi-grid methods for Stokes and Navier-Stokes equations. Transforming smoothers: Algorithms and numerical results
type: Item
instance of: scholarly article
title: Multi-grid methods for Stokes and Navier-Stokes equations. Transforming smoothers: Algorithms and numerical results
zbMATH Open document ID: 0645.76031
DOI: 10.1007/BF01396361
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133332
review text: In the present paper we introduce transforming iterations, an approach to construct smoothers for indefinite systems. This turns out to be a convenient tool to classify several well-known smoothing iterations for Stokes and Navier-Stokes equations and to predict their convergence behaviour, especially in the case of high Reynolds-numbers. Using this approach, we are able to construct a new smoother for the Navier-Stokes equations, based on incomplete LU-decompositions, yielding a highly effective and robust multi-grid method. Besides some qualitative theoretical convergence results, we give large numerical comparisons and tests for the Stokes as well as for the Navier-Stokes equations.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65F10
zbMATH DE Number: 4053186
zbMATH Keywords: transforming iterations
zbMATH Keywords: smoothers for indefinite systems
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: incomplete LU-decompositions
zbMATH Keywords: multi-grid method
zbMATH Keywords: convergence
zbMATH Keywords: distributive smoothing
author: G. Wittum
MaRDI profile type: Publication
cites work: A stable finite element for the Stokes equations
cites work: Q4734923
cites work: Corrigenda
cites work: Q3703469
cites work: Q3893527
cites work: Q4105995
cites work: Q3345961
cites work: Finite Element Methods for Navier-Stokes Equations
cites work: Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems
cites work: Q3727300
cites work: Q3750065
cites work: Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface
cites work: Q5768822
cites work: Q3730276
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
cites work: A calculation procedure for heat, mass and momentum transfer in three- dimensional parabolic flows
cites work: Driven cavity flows by efficient numerical techniques
cites work: A calculation procedure for three-dimensional steady recirculating flows using multigrid methods
cites work: Q5342712
cites work: A posteriori error estimators for the Stokes equations
cites work: Theoretical and Practical Aspects of a Multigrid Method
cites work: Q3761622
cites work: On the convergence of multi-grid methods with transforming smoothers
cites work: On the Robustness of ILU Smoothing
description: scientific article; zbMATH DE number 4053186