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A dissipation-preserving finite element method for nonlinear fractional wave equations on irregular convex domains

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  • Li, Meng
  • Fei, Mingfa
  • Wang, Nan
  • Huang, Chengming

Abstract

In this manuscript, we consider an efficient dissipation-preserving finite element method for a class of two-dimensional nonlinear fractional wave equations on irregular convex domains. We show that the fully discrete method preserves the discrete energy structures under the same boundary conditions as the continuous model. Furthermore, the optimal order error estimates of the fully discrete scheme are proved in detail. Finally, the numerical simulations, which are based on spatial unstructured meshes, are presented to confirm the correctness of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:404-419
    DOI: 10.1016/j.matcom.2020.05.005
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    References listed on IDEAS

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    1. Dehghan, Mehdi & Shokri, Ali, 2008. "A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 700-715.
    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.
    3. Liu, Zeting & Lü, Shujuan & Liu, Fawang, 2018. "Fully discrete spectral methods for solving time fractional nonlinear Sine–Gordon equation with smooth and non-smooth solutions," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 213-224.
    4. Wang, Junjie & Xiao, Aiguo, 2019. "Conservative Fourier spectral method and numerical investigation of space fractional Klein–Gordon–Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 348-365.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.

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