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A note on Reusken's Lemma

Eine Bemerkung zum Lemma von Reusken

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Abstract

A modification of the Lemma of Reusken is given. It allows us to improve the estimate of the smoothing property in cases where the contraction number of the iteration is small. This is of importance for robust multi-grid methods. Moreover, we describe a simple semi-iterative smoother with better asymptotic behaviour than for the stationary iterative smoother.

Zusammenfassung

Eine Modifikation des Lemmas von Reusken wird angegeben. Sie gestattet, im Falle von konvergenten Glättungsiterationen die Konvergenzgeschwindigkeit in die Abschätzung der Glättungseigenschaft mit aufzunehmen. Eine derartige Abschätzung wird bei robusten Mehrgitterverfahren benötigt. Ferner wird ein einfacher semiiterativer Glätter angegeben, der ein asymptotisch besseres Verhalten besitzt.

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Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität zu Kiel, Olshausenstrasse 40, D-24098, Kiel, Germany

    W. Hackbusch

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  1. W. Hackbusch
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Hackbusch, W. A note on Reusken's Lemma. Computing 55, 181–189 (1995). https://doi.org/10.1007/BF02238100

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  • DOI: https://doi.org/10.1007/BF02238100

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