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- W2802461736 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 $kge 2$ 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." @default.
- W2802461736 created "2018-05-17" @default.
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- W2802461736 date "2018-05-09" @default.
- W2802461736 modified "2023-09-26" @default.
- W2802461736 title "An energy-conserving ultra-weak discontinuous Galerkin method for the generalized Korteweg-De Vries equation" @default.
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- W2802461736 doi "https://doi.org/10.48550/arxiv.1805.04471" @default.
- W2802461736 hasPublicationYear "2018" @default.
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