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Some remarks on the discrete maximum-principle for finite elements of higher order

Bemerkungen zum diskreten Maximumprinzip für Finite Elemente höherer Ordnung

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Abstract

The discrete maximum principle for finite element approximations of standard elliptic problems in the plane is discussed. Even in the case Δu=0 a slightly stronger version of the principle does not hold with piecewise quadratic elements for all but some very special triangularisation geometries.

Zusammenfassung

Diskutiert wird das diskrete Maximumprinzip für Finite-Element-Approximationen von elliptischen Standardproblemen in der Ebene. Schon im Fall Δu=0 treten bei stückweise quadratischen Elementen Verletzungen einer leicht verschärften Version des Prinzips auf, außer in einigen ganz speziellen Triangulierungsgeometrien.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-6100, Darmstadt, Federal Republic of Germany

    W. Höhn

  2. Abteilung Mathematik, Universität Dortmund, Postfach 500500, D-4600, Dortmund 50, Federal Republic of Germany

    H. D. Mittelmann

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  1. W. Höhn
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  2. H. D. Mittelmann
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Höhn, W., Mittelmann, H.D. Some remarks on the discrete maximum-principle for finite elements of higher order. Computing 27, 145–154 (1981). https://doi.org/10.1007/BF02243548

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  • DOI: https://doi.org/10.1007/BF02243548

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