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arXiv · 1805.04471

An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation

Guosheng Fu·Chi-Wang Shu
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Abstract

We propose an energy-conserving ultra-weak discontinuous Galerkin (DG) method for the generalized Korteweg-De Vries(KdV) equation in one dimension. Optimal a priori error estimate of order $k + 1$ is obtained for the semi-discrete scheme for the KdV equation without convection term on general nonuniform meshes when polynomials of degree $k\ge 2$ is used. We also numerically observed optimal convergence of the method for the KdV equation with linear or nonlinear convection terms. It is numerically observed for the new method to have a superior performance for long-time simulations over existing DG methods.

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Guosheng Fu, Chi-Wang Shu. 2018-05-10. An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation. https://arxiv.org/abs/1805.04471

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