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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… Click to show full 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 L 2 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.
Journal Title: Numerical Algorithms
Year Published: 2022
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