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Multi-grid methods for stokes and navier-stokes equations

Transforming smoothers: algorithms and numerical results

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Summary

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].

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  1. Sonderforschungsbereich 123, Universität Heidelberg, Im Neuenheimer Feld 294, D-6900, Heidelberg, Federal Republic of Germany

    G. Wittum

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  1. G. Wittum
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This work was supported in part by Deutsche Forschungsgemeinschaft

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Wittum, G. Multi-grid methods for stokes and navier-stokes equations. Numer. Math. 54, 543–563 (1989). https://doi.org/10.1007/BF01396361

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