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A Dirichlet–Neumann cost functional approach for the Bernoulli problem

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Abstract

The Bernoulli problem is rephrased into a shape optimization problem. In particular, the cost function, which turns out to be a constitutive law gap functional, is borrowed from inverse problem formulations. The shape derivative of the cost functional is explicitly determined. The gradient information is combined with the level set method in a steepest descent algorithm to solve the shape optimization problem. The efficiency of this approach is illustrated by numerical results for both interior and exterior Bernoulli problems.

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Authors and Affiliations

  1. Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur (LAMSIN), El Manar University, Tunis, Tunisia

    A. Ben Abda & M. Sayeh

  2. Laboratoire de Mathématiques, Clermont Université, Université Blaise Pascal, BP10448, 63000 , Clermont-Ferrand, France

    F. Bouchon & R. Touzani

  3. Laboratoire de Mathématiques, CNRS, UMR 6620, 63177 , Aubiere, France

    F. Bouchon & R. Touzani

  4. Institute for Mathematics and Scientific Computing, University of Graz, Heinrichstr. 36, 8010,  Graz, Austria

    G. H. Peichl

Authors
  1. A. Ben Abda
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  2. F. Bouchon
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  3. G. H. Peichl
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  4. M. Sayeh
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  5. R. Touzani
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Correspondence to F. Bouchon.

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Ben Abda, A., Bouchon, F., Peichl, G.H. et al. A Dirichlet–Neumann cost functional approach for the Bernoulli problem. J Eng Math 81, 157–176 (2013). https://doi.org/10.1007/s10665-012-9608-3

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  • DOI: https://doi.org/10.1007/s10665-012-9608-3

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