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Numerical Analysis and Simulation for a Wave Equation with Dynamical Boundary Control

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Abstract

This paper is concerned with a theoretical and numerical analysis for the stability of a vibrating beam of finite length which is fixed at one end and free at the other end and with a dynamical boundary control. On the theoretical results, we prove the existence and uniquenes of global solutions, and the stability of the total energy. Furthemore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time. Error estimates fot the semi-discrete and fully discrete schemes are provided and numerical experiments performed. From the numerical results, the rate of convergence are shoown to be consistent with the order of convegence expected from the theoretical ones.

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Acknowledgements

The author M.A. Rincon is partially supported by CNPq-Brasil under Grant 301788/2016-2.

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Authors and Affiliations

  1. Faculty of Sciences, Beirut Arab University, Beirut, Lebanon

    Moussa Bzeih & Toufic El Arwadi

  2. Faculty of Sciences, Lebanese University, KALMA, Hadath-Beirut, Lebanon

    Ali Wehbe

  3. Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Mauro A. Rincon

  4. NCE/PPGI, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Rodrigo L. R. Madureira

Authors
  1. Moussa Bzeih
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  2. Toufic El Arwadi
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  3. Ali Wehbe
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  4. Mauro A. Rincon
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  5. Rodrigo L. R. Madureira
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Correspondence to Moussa Bzeih.

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Bzeih, M., El Arwadi, T., Wehbe, A. et al. Numerical Analysis and Simulation for a Wave Equation with Dynamical Boundary Control. J Sci Comput 87, 6 (2021). https://doi.org/10.1007/s10915-021-01408-z

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  • DOI: https://doi.org/10.1007/s10915-021-01408-z

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