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Numerical Methods for the Vector-Valued Solutions of Non-smooth Eigenvalue Problems

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Abstract

In this article, we address the numerical solution of non-smooth eigenvalue problems coming from continuum mechanics. These problems have applications in plasticity theory, since the smallest eigenvalue of the non-smooth operators under consideration appears in the estimation of the cut-off time of some Bingham flows. Three vector-valued eigenvalue problems are investigated. The case of divergence free functions is included. Piecewise linear finite elements are used for the discretization of the eigenfunctions. An augmented Lagrangian method is proposed for the solution of the associated non-convex optimization problem. Numerical solutions are presented for the first eigenpair of these problems and convergence orders are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, 4800 Calhoun Rd, Houston, TX, 77204-3008, USA

    Alexandre Caboussat & Roland Glowinski

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  1. Alexandre Caboussat
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  2. Roland Glowinski
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Correspondence to Alexandre Caboussat.

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In memory of Professor David Gottlieb.

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Caboussat, A., Glowinski, R. Numerical Methods for the Vector-Valued Solutions of Non-smooth Eigenvalue Problems. J Sci Comput 45, 64–89 (2010). https://doi.org/10.1007/s10915-010-9383-0

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  • DOI: https://doi.org/10.1007/s10915-010-9383-0

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