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The Inverse Power Method for the \(p(x)\)-Laplacian Problem

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Abstract

We present an inverse power method for the computation of the first homogeneous eigenpair of the \(p(x)\)-Laplacian problem. The operators are discretized by the finite element method. The inner minimization problems are solved by a globally convergent inexact Newton method. Numerical comparisons are made, in one- and two-dimensional domains, with other results present in literature for the constant case \(p(x)\equiv p\) and with other minimization techniques (namely, the nonlinear conjugate gradient) for the \(p(x)\) variable case.

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Acknowledgments

The authors cordially thank Dr. Stefan Rainer for the helpful discussions about numerical methods for unconstrained minimization.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Strada Le Grazie 15, 37134, Verona, Italy

    M. Caliari & S. Zuccher

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  1. M. Caliari
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  2. S. Zuccher
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Correspondence to M. Caliari.

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Caliari, M., Zuccher, S. The Inverse Power Method for the \(p(x)\)-Laplacian Problem. J Sci Comput 65, 698–714 (2015). https://doi.org/10.1007/s10915-015-9982-x

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  • DOI: https://doi.org/10.1007/s10915-015-9982-x

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