A local discontinuous Galerkin method for the Novikov equation

Tao, Qi; Chang, Xiang-Ke; Liu, Yong; Shu, Chi-Wang

doi:10.1090/mcom/4018

A local discontinuous Galerkin method for the Novikov equation
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by Qi Tao, Xiang-Ke Chang, Yong Liu and Chi-Wang Shu;

Math. Comp. 94 (2025), 1603-1631

DOI: https://doi.org/10.1090/mcom/4018

Published electronically: September 6, 2024

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Abstract:

In this paper, we propose a local discontinuous Galerkin (LDG) method for the Novikov equation that contains cubic nonlinear high-order derivatives. Flux correction techniques are used to ensure the stability of the numerical scheme. The $H^1$-norm stability of the general solution and the error estimate for smooth solutions without using any priori assumptions are presented. Numerical examples demonstrate the accuracy and capability of the LDG method for solving the Novikov equation.

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Mathematics of Computation

A local discontinuous Galerkin method for the Novikov equation
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Abstract: