# 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} }

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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