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An iterative finite element method using the Kantorovich technique

Eine iterative Methode der finiten Elemente unter Verwendung der Methode von Kantorowitsch

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Summary

The extended Kantorovich method of variational calculus is used as the basis of a finite element method. This method has wide applicability in many fields of study; such as soil mechanics, vibration of membranes, fluid mechanics etc. Here the method is applied to the problem of magneto-hydrodynamic (MHD) duct flow, and excellent agreement is found between the obtained results and the analytical solution. Several of the disadvantages inherent in the usual form of the extended Kantorovich method are discussed, and means of overcoming them presented.

Zusammenfassung

Die erweiterte Methode von Kantorowitsch dient als Ausgangspunkt der Methode der finiten Elemente. Diese Methode bietet ein breites Spektrum von Anwendungsgebieten, wie Bodenmechanik, Membranschwingungen, Strömungsprobleme usw. Sie wird hier auf ein Problem der magneto-gasdynamischen Rohrströmung angewendet und ausgezeichnete Übereinstimmung zwischen den so erhaltenen und analytischen Resultaten erhalten. Einige der in üblichen Anwendung der erweiterten Methode von Kantorowitsch auftretenden Nachteile werden erörtert, einschließlich von Möglichkeiten, diese zu umgehen.

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Authors and Affiliations

  1. Dept. of Applied Mathematics, University of Witwatersrand, Johannesburg, South Africa

    R. Jones

  2. Dept. of Civil Engineering, Swinburne College of Techrnology, Hawthorn, Victoria, Australia

    J. Xenophontos

Authors
  1. R. Jones
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  2. J. Xenophontos
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Jones, R., Xenophontos, J. An iterative finite element method using the Kantorovich technique. Acta Mechanica 26, 91–101 (1977). https://doi.org/10.1007/BF01177138

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  • DOI: https://doi.org/10.1007/BF01177138

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