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LDG scheme for first-order hyperbolic systems with time-fractional dissipation on graded meshes

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  • Li, Can
  • Hou, Zexin

Abstract

In this paper, we design and analyze local discontinuous Galerkin (LDG) schemes with αβ-fluxes for hyperbolic problems involving fractional dissipation. The numerical fluxes in our discontinuous Galerkin method are based on the work of Cheng et al. (2017). Using these fluxes, we derive error estimates for both the semi-discrete and fully discrete LDG schemes applied to the model under consideration. The fully discrete scheme combines the LDG method for spatial discretization with a fast L1 approximation on a graded mesh for temporal discretization. We perform stability analyses in the L2-norm for both the semi-discrete and fully discrete schemes, demonstrating that they are unconditionally stable and achieve optimal convergence rates. Finally, numerical experiments are presented to validate the accuracy and efficiency of the proposed methods.

Suggested Citation

  • Li, Can & Hou, Zexin, 2026. "LDG scheme for first-order hyperbolic systems with time-fractional dissipation on graded meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 246(C), pages 779-804.
    • Handle: RePEc:eee:matcom:v:246:y:2026:i:c:p:779-804
    DOI: 10.1016/j.matcom.2026.03.007
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    References listed on IDEAS

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    1. Sun, Xiaorui & Li, Can & Zhao, Fengqun, 2020. "Local discontinuous Galerkin methods for the time tempered fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    2. Meilan Qiu & Dewang Li & Yanyun Wu, 2020. "Local Discontinuous Galerkin Method for Nonlinear Time-Space Fractional Subdiffusion/Superdiffusion Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-21, June.
    3. Wei, Leilei, 2017. "Analysis of a new finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation," Applied Mathematics and Computation, Elsevier, vol. 304(C), pages 180-189.
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