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Conservative and dissipative local discontinuous Galerkin methods for Korteweg-de Vries type equations

Qian Zhang University of Science and Technology of China Yinhua Xia University of Science and Technology of China

Numerical Analysis and Scientific Computing mathscidoc:1903.25006

Communications in Computional Physics, 25, 532-563, 2019.10
In this paper, we develop the Hamiltonian conservative and L2 conservative local discontinuous Galerkin (LDG) schemes for the Korteweg-de Vries (KdV) type equations with the minimal stencil. For the time discretization, we adopt the semi- implicit spectral deferred correction (SDC) method to achieve the high order accuracy and efficiency. Also we compare the schemes with the dissipative LDG scheme. Stabil- ity of the fully discrete schemes is provided by Fourier analysis for the linearized KdV equation. Numerical examples are shown to illustrate the capability of these schemes. Compared with the dissipative LDG scheme, the numerical simulations also indicate that the conservative LDG scheme with high order time discretization can reduce the long time phase error validly.
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@inproceedings{qian2019conservative,
  title={Conservative and dissipative local discontinuous Galerkin methods for Korteweg-de Vries type equations},
  author={Qian Zhang, and Yinhua Xia},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190323095141967862223},
  booktitle={Communications in Computional Physics},
  volume={25},
  pages={532-563},
  year={2019},
}
Qian Zhang, and Yinhua Xia. Conservative and dissipative local discontinuous Galerkin methods for Korteweg-de Vries type equations. 2019. Vol. 25. In Communications in Computional Physics. pp.532-563. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190323095141967862223.
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