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Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem

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Abstract

Some conforming, nonconforming and mixed finite element methods for approximating the clamped plate problem

$$\Delta ^2 u = f in \Omega , u = \partial u/\partial n = o on \partial \Omega ,$$

on ∂Ω, over a bounded plane domain Ω ⊂R2 are considered. Asymptotic L∞-estimates for the error in displacement are established which have the same 0(h)-order as the well known L2-estimates. As in the case of second order problems (see [7]) the proofs rest on estimates for regularized fundamental solutions of the operator Δ2 and its discrete analogues.

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  1. Institut für Angewandte Mathematik, der Universität Bonn, Beringstraße 4-6, D-5300, Bonn

    Rolf Rannacher

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  1. Rolf Rannacher
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Rannacher, R. Punktweise Konvergenz der Methode der finiten Elemente beim Plattenproblem. Manuscripta Math 19, 401–416 (1976). https://doi.org/10.1007/BF01278927

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  • DOI: https://doi.org/10.1007/BF01278927

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