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Numerical Approximation of a Unilateral Obstacle Problem

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Abstract

We consider a reformulation of the unilateral obstacle problem presented by the authors (Addou and Mermri in Math-Rech. Appl. 2:59–69, 2000). This reformulation introduces a continuous function, whose subdifferential characterizes the noncontact domain. Our goal in this paper is to give a numerical approximation of the solution of the reformulated problem. We consider discretization of the problem based on finite element method. Then we prove the convergence of the approximate solution to the exact one. Some numerical tests on one-dimensional obstacle problem are provided.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science, University Mohammed Premier, 60050, Oujda, Morocco

    E. B. Mermri

  2. Department of Mathematics, University of Iowa, Iowa City, IA, 52242, USA

    W. Han

Authors
  1. E. B. Mermri
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  2. W. Han
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Correspondence to E. B. Mermri.

Additional information

Communicated by Francesco Zirilli.

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Mermri, E.B., Han, W. Numerical Approximation of a Unilateral Obstacle Problem. J Optim Theory Appl 153, 177–194 (2012). https://doi.org/10.1007/s10957-011-9956-6

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  • DOI: https://doi.org/10.1007/s10957-011-9956-6

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