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Anisotropic interpolation with applications to the finite element method

Anisotrope Interpolation mit Anwendungen auf die finite Elemente Methode

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Abstract

The usual Bramble-Hilbert theory is extended for proving more refined estimates of the interpolation error. For a large class of finite elements, it is shown that one can derive benefit from the presence of small and even large angles of the elements. For bilinear shape functions on rectangular grids it is proved that interpolation and finite element approximation error coincide. As an example, we consider the finite element approximation for problems on domains containing edges.

Zusammenfassung

Die bekannte Bramble-Hilbert Theorie wird erweitert, um verbesserte Abschätzungen für den Interpolationsfehler zu beweisen. Für eine große Klasse finiter Elemente läßt sich zeigen, daß man mit Dreiecken mit kleinem oder sogar großem Winkel vorteilhafter interpolieren kann. Für bilineare Ansatzfunktionen auf rechteckigem Gitter wird bewiesen, daß der Interpolationsfehler mit dem Approximationsfehler übereinstimmt. Als Anwendungsbeispiel wird die Finite Elemente Approximation von Problemen auf Gebieten mit Kanten betrachtet.

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Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Technische Hochschule Zwickau, Dr.-Friedrichs-Ring 2a, D-O-9541, Zwickau, Federal Republic of Germany

    T. Apel

  2. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, D-W-8520, Erlangen, Federal Republic of Germany

    M. Dobrowolski

Authors
  1. T. Apel
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  2. M. Dobrowolski
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Apel, T., Dobrowolski, M. Anisotropic interpolation with applications to the finite element method. Computing 47, 277–293 (1992). https://doi.org/10.1007/BF02320197

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  • DOI: https://doi.org/10.1007/BF02320197

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