IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v205y2023icp315-339.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422004013
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.09.024?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Nan & Shi, Dongyang, 2021. "Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 696-718.
    2. Li, Meng & Wei, Yifan & Niu, Binqian & Zhao, Yong-Liang, 2022. "Fast L2-1σ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    3. Hu, Dongdong & Cai, Wenjun & Xu, Zhuangzhi & Bo, Yonghui & Wang, Yushun, 2021. "Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine–Gordon equation with damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 35-59.
    4. You, Xiangcheng & Xu, Hang & Sun, Qiang, 2022. "Analysis of BBM solitary wave interactions using the conserved quantities," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. 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.
    6. Almushaira, Mustafa, 2023. "An efficient fourth-order accurate conservative scheme for Riesz space fractional Schrödinger equation with wave operator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 424-447.
    7. Fu, Yayun & Song, Yongzhong & Wang, Yushun, 2019. "Maximum-norm error analysis of a conservative scheme for the damped nonlinear fractional Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 206-223.
    8. Zou, Guang-an & Wang, Bo & Sheu, Tony W.H., 2020. "On a conservative Fourier spectral Galerkin method for cubic nonlinear Schrödinger equation with fractional Laplacian," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 168(C), pages 122-134.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:315-339. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.