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Successive overrelaxation method with projection for finite element solutions applied to the Dirichlet problem of the nonlinear elliptic equation Δu-bu2

Sukzessive Überrelaxationsverfahren mit Projektion zu finiten Elementlösungen für das Dirichletsche Problem bei der nichtlinearen elliptischen Differentialgleichung Δu=bu2

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Abstract

this study is a continuation of a previous paper [Computing 38 (1987), pp.117–132]. In this paper, we consider the successive overrelaxation method with projection for obtaining finite element solutions applied to the Dirichlet problem of the nonlinear elliptic equation

$$\begin{gathered} \Delta u = bu^2 in\Omega , \hfill \\ u = g(x)on\Gamma . \hfill \\ \end{gathered} $$

. Some numerical examples are given to illustrate the effectiveness.

Zusammenfassung

Diese Veröffentlichung ist eine Fortsetzung einer früheren Studie [Computing 38 (1987), S. 117–132]. In dieser Arbeit wird das sukzessive Überrelaxationsverfahren mit Projektion zu finiten Elementlösungen für das Dirichletsche Problem

$$\begin{gathered} \Delta u = bu^2 in\Omega , \hfill \\ u = g(x)auf \Gamma . \hfill \\ \end{gathered} $$

beachtet. An einigen numerischen Beispielen wird die Effektivität aufgezeigt.

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  1. Department of Mathematics, Kyushu Institute of Technology, 804, Tobata, Kitakyushu, Japan

    K. Ishihara

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Ishihara, K. Successive overrelaxation method with projection for finite element solutions applied to the Dirichlet problem of the nonlinear elliptic equation Δu-bu2 . Computing 40, 51–65 (1988). https://doi.org/10.1007/BF02242189

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