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Explicit monotone iterations providing upper and lower bounds for finite element solution with nonlinear radiation boundary conditions

Explizites monotones Iterationsverfahren mit oberen und unteren Schranken zur finiten Element-Lösung mit nichtlinearen Radiationsrandbedingungen

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Abstract

In this paper we consider explicit monotone iterations of the finite element solutions for the radiation cooling problem with the nonlinear boundary conditions. These iterations provide upper and lower bounds, and convergence proofs are given. Finally, we give some numerical examples to demonstrate the effectiveness.

Zusammenfassung

In dieser Arbeit beobachten wir das explizite monotone Iterationsverfahren von finiten Elementlösungen für das Radiationskühlungsproblem mit nichtlinearen Randbedingungen. Bei diesem Iterationsverfahren ergeben sich obere und untere Schranken, und eine Konvergenz kann nachgewiesen werden. An einigen numerischen Beispielen wird die Brauchbarkeit gezeigt.

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

    K. Ishihara

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  1. K. Ishihara
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Ishihara, K. Explicit monotone iterations providing upper and lower bounds for finite element solution with nonlinear radiation boundary conditions. Computing 37, 137–149 (1986). https://doi.org/10.1007/BF02253187

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