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• W3205803884 abstract "Boussinesq type equations have been widely studied to model the surface water wave. In this paper, we consider the abcd Boussinesq system which is a family of Boussinesq type equations including many well-known models such as the classical Boussinesq system, BBM-BBM system, Bona-Smith system etc. We propose local discontinuous Galerkin (LDG) methods, with carefully chosen numerical fluxes, to numerically solve this abcd Boussinesq system. The main focus of this paper is to rigorously establish a priori error estimate of the proposed LDG methods for a wide range of the parameters a, b, c, d. Numerical experiments are shown to test the convergence rates, and to demonstrate that the proposed methods can simulate the head-on collision of traveling wave and finite time blow-up behavior well." @default.
• W3205803884 created "2021-10-25" @default.
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• W3205803884 date "2021-10-08" @default.
• W3205803884 modified "2023-09-26" @default.
• W3205803884 title "Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system" @default.
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• W3205803884 doi "https://doi.org/10.48550/arxiv.2110.04339" @default.
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