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A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods

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An Erratum to this article was published on 01 June 1990

Abstract

In this paper we discuss the numerical implementation of a systematic method for the exact boundary controllability of the wave equation, concentrating on the particular case of Dirichlet controls. The numerical methods described here consist in a combination of: finite element approximations for the space discretization; explicit finite difference schemes for the time discretization; a preconditioned conjugate gradient algorithm for the solution of the discrete problems; a pre/post processing technique based on a biharmonic Tychonoff regularization. The efficiency of the computational methodology is illustrated by the results of numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics, University of Houston, 4800 Calhoun Road, 77004, Houston, Texas, U.S.A.

    Roland Glowinski

  2. INRIA, France

    Roland Glowinski

  3. Department of Mathematics, University of Houston, Houston, USA

    Chin-Hsien Li

  4. Collège de France, 3 Rue d’Ulm, 75, Paris 5, France

    Jacques-Louis Lions

  5. CNES, Paris, France

    Jacques-Louis Lions

Authors
  1. Roland Glowinski
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  2. Chin-Hsien Li
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  3. Jacques-Louis Lions
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Additional information

Dedicated to Jim Douglas for his 60th Birthday

An erratum to this article is available at http://dx.doi.org/10.1007/BF03167859.

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Glowinski, R., Li, CH. & Lions, JL. A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods. Japan J. Appl. Math. 7, 1–76 (1990). https://doi.org/10.1007/BF03167891

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  • DOI: https://doi.org/10.1007/BF03167891

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