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Numerische Behandlung nichtlinearer Randwertprobleme mit finiten Elementen

Numerical treatment of nonlinear boundary-value problems by finite elements

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Zusammenfassung

Es werden gemischte Randwertprobleme quasilinearer gleichmäßig elliptischer Differentialgleichungen behandelt sowie das Minimalflächenproblem. Die Lösung wird mit Hilfe der einfachsten Methode der finiten Elemente approximiert. Das nicht notwendigerweise konvexe Gebiet wird hierzu mit einem im Innern gleichmäßigen Dreiecksgitter bedeckt. Für alle betrachteten Probleme wird Konvergenz, auch in der Maximumnorm, bewiesen. Numerische Ergebnisse für eine Minimal- und eine Kapillarfläche werden angegeben.

Abstract

Mixed boundary-value problems are considered for quasilinear uniformly elliptic differential equations as well as the minimal surface problem. The solution is approximated by the simplest finite element method. Assuming that the triangulation is uniform in the interior of the not necessarily convex domain, convergence is proved for all problems including pointwise estimates. Numerical results are given for a minimal and a capillary surface.

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Literatur

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D-6100, Darmstadt, Bundesrepublik Deutschland

    H. D. Mittelmann

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  1. H. D. Mittelmann
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Mittelmann, H.D. Numerische Behandlung nichtlinearer Randwertprobleme mit finiten Elementen. Computing 18, 67–77 (1977). https://doi.org/10.1007/BF02248778

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  • DOI: https://doi.org/10.1007/BF02248778

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