Optimal Error Estimates of the Local Discontinuous Galerkin Method with Generalized Numerical Fluxes for One-Dimensional KdV Type Equations
Year: 2025
Author: Hongjuan Zhang, Xiong Meng, Dazhi Zhang, Boying Wu
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 63–88
Abstract
In this paper, we investigate the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear Korteweg-de Vries type equations. The numerical flux for the nonlinear convection term is chosen as the generalized Lax-Friedrichs flux, and the generalized alternating flux and upwind-biased flux are used for the dispersion term. The generalized Lax-Friedrichs flux with anti-dissipation property will compensate the numerical dissipation of the dispersion term, resulting in a nearly energy conservative scheme that is useful in resolving waves and is beneficial for long time simulations. To deal with the nonlinearity and different numerical flux weights, a suitable numerical initial condition is constructed, for which a modified global projection is designed. By establishing relationships between the prime variable and auxiliary variables in combination with sharp bounds for jump terms, optimal error estimates are obtained. Numerical experiments are shown to confirm the validity of theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2307-m2022-0278
Journal of Computational Mathematics, Vol. 43 (2025), Iss. 1 : pp. 63–88
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Korteweg-de Vries type equations Local discontinuous Galerkin method Generalized fluxes Error estimates.
Author Details
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Analysis of the Local Discontinuous Galerkin Method with Generalized Numerical Fluxes for One-Dimensional Nonlinear Fourth-Order Time-Dependent Problems
Li, Linhui
Meng, Xiong
Li, Jia
Journal of Scientific Computing, Vol. 102 (2025), Iss. 3
https://doi.org/10.1007/s10915-025-02800-9 [Citations: 0]