Local discontinuous Galerkin method for a nonlocal viscous water wave model

In this article, the fully discrete local discontinuous Galerkin (LDG) method is presented for numerically solving a class of nonlocal viscous water wave model, where the BDF2 with the L1 formula of the time Caputo fractional derivative is applied to deal with the time direction, and the LDG method is developed to approximate the space direction. The stability of the fully discrete LDG scheme is proven, and the a priori error result with 3 O (& tau; 2 + hk+12 ) in L2-norm is derived in detail. Finally, numerical examples supporting theoretical error result are provided, and the decay rates under different coefficients are also discussed. & COPY; 2023 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This article presents the fully discrete local discontinuous Galerkin (LDG) method for numerically solving a class of nonlocal viscous water wave model. The BDF2 with the L1 formula of the time Caputo fractional derivative is used for the time direction, and the LDG method is used for the space direction approximation. The stability of the fully discrete LDG scheme is proven, and a detailed a priori error result with 3 O (τ 2 + hk+12 ) in L2-norm is derived. Numerical examples supporting the theoretical error result are provided, and the decay rates under different coefficients are also discussed.