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A mass- and energy-conserved DG method for the Schrödinger-Poisson equation

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Abstract

We construct, analyze, and numerically validate a class of conservative discontinuous Galerkin (DG) schemes for the Schrödinger-Poisson equation. The proposed schemes all shown to conserve both mass and energy. For the semi-discrete DG scheme the optimal L2 error estimates are provided. Efficient iterative algorithms are also constructed to solve the second-order implicit time discretization. The presented numerical tests demonstrate the method’s accuracy and robustness, confirming that the conservation properties help to reproduce faithful solutions over long time simulation.

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Funding

Yi’s research was partially supported by NSFC Project (11671341, 11971410) and Hunan Provincial NSF Project (2019JJ20016).

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Authors and Affiliations

  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering; School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, People’s Republic of China

    Nianyu Yi

  2. Iowa State University, Mathematics Department, Ames, IA, 50011, USA

    Hailiang Liu

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  1. Nianyu Yi
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  2. Hailiang Liu
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Correspondence to Hailiang Liu.

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Yi, N., Liu, H. A mass- and energy-conserved DG method for the Schrödinger-Poisson equation. Numer Algor 89, 905–930 (2022). https://doi.org/10.1007/s11075-021-01139-0

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  • DOI: https://doi.org/10.1007/s11075-021-01139-0

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