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

Can Li and Zexin Hou

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 246, issue C, 779-804

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.

Keywords: Local discontinuous Galerkin methods; First-order hyperbolic system; Stability; Convergence (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:246:y:2026:i:c:p:779-804

DOI: 10.1016/j.matcom.2026.03.007

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