Computing

, Volume 27, Issue 2, pp 145–154 | Cite as

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

  • W. Höhn
  • H. D. Mittelmann
Article
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Revised:

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.

Keywords

Computational Mathematic Maximum Principle Elliptic Problem Element Approximation Strong Version 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bemerkungen zum diskreten Maximumprinzip für Finite Elemente höherer Ordnung

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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References

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • W. Höhn
    • 1
  • H. D. Mittelmann
    • 2
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtFederal Republic of Germany
  2. 2.Abteilung MathematikUniversität DortmundDortmund 50Federal Republic of Germany

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