Corpus ID: 237513407

A discontinuous Galerkin method for nonlinear biharmonic Schr\"{o}dinger equations

@inproceedings{Zhang2021ADG,
  title={A discontinuous Galerkin method for nonlinear biharmonic Schr\"\{o\}dinger equations},
  author={Lu Zhang},
  year={2021}
}
  • Lu Zhang
  • Published 15 September 2021
  • Mathematics, Computer Science
This paper proposes and analyzes an ultra-weak local discontinuous Galerkin scheme for one-dimensional nonlinear biharmonic Schrödinger equations. We develop the paradigm of the local discontinuous Galerkin method by introducing the second-order spatial derivative as an auxiliary variable instead of the conventional first-order derivative. The proposed semi-discrete scheme preserves a few physically relevant properties such as the conservation of mass and the conservation of Hamiltonian… Expand

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