Multi-grid methods for stokes and navier-stokes equations - Transforming smoothers: algorithms and numerical results

Gabriel Wittum*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

100 Scopus citations

Abstract

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, epecially 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. For a general convergence theory we refer to [29].

Original languageEnglish (US)
Pages (from-to)543-563
Number of pages21
JournalNumerische Mathematik
Volume54
Issue number5
DOIs
StatePublished - Sep 1 1989

Keywords

  • Subject Classifications: AMS(MOS):65N20, CR:G1.8

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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