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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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