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A finite element scheme for a 2D-wave equation with dynamical boundary control

Author

Listed:
  • Bzeih, Moussa
  • Arwadi, Toufic El
  • Wehbe, Ali
  • Madureira, Rodrigo L.R.
  • Rincon, Mauro A.

Abstract

We study the 2D linear wave equation with dynamical control on the boundary. New mathematical difficulties appear due to the boundary conditions. By adding some artificial viscosity term, we introduce a penalized problem, and the well posedness is done by using the Faedo–Galerkin method. A numerical scheme is proposed and the decay of the associated discrete energy is obtained. At the end, an a priori error estimate is obtained and some numerical results are presented.

Suggested Citation

  • Bzeih, Moussa & Arwadi, Toufic El & Wehbe, Ali & Madureira, Rodrigo L.R. & Rincon, Mauro A., 2023. "A finite element scheme for a 2D-wave equation with dynamical boundary control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 315-339.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:315-339
    DOI: 10.1016/j.matcom.2022.09.024
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    References listed on IDEAS

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    1. Li, Meng & Fei, Mingfa & Wang, Nan & Huang, Chengming, 2020. "A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 404-419.
    2. Li, Meng & Zhao, Yong-Liang, 2018. "A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 758-773.
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