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 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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Tao et al. (2024) studied this question.
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