Authors

Wensheng Tang, Yajuan Sun, Wenjun Cai

Abstract

In this article, we present a unified framework of discontinuous Galerkin (DG) discretizations for Hamiltonian ODEs and PDEs. We show that with appropriate numerical fluxes the numerical algorithms deduced from DG discretizations can be combined with the symplectic methods in time to derive the multi-symplectic PRK schemes. The resulting numerical discretizations are applied to the linear and nonlinear Schrödinger equations. Some conservative properties of the numerical schemes are investigated and confirmed in the numerical experiments.

Keywords

Discontinuous Galerkin method; Hamiltonian systems; Continuous-stage PRK method; Symplectic PRK scheme; Multi-symplectic PRK scheme; Conservation laws

Citation

  • Journal: Journal of Computational Physics
  • Year: 2017
  • Volume: 330
  • Issue:
  • Pages: 340–364
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.jcp.2016.11.023

BibTeX

@article{Tang_2017,
  title={{Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs}},
  volume={330},
  ISSN={0021-9991},
  DOI={10.1016/j.jcp.2016.11.023},
  journal={Journal of Computational Physics},
  publisher={Elsevier BV},
  author={Tang, Wensheng and Sun, Yajuan and Cai, Wenjun},
  year={2017},
  pages={340--364}
}

Download the bib file

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