Optimal Error Estimates of Conservative Local Discontinuous Galerkin Method for Nonlinear Schrödinger Equation
This work provides a rigorous convergence analysis for a conservative numerical method for the nonlinear Schrödinger equation, which is important for computational physics.
The authors propose a conservative local discontinuous Galerkin method for the 1D nonlinear Schrödinger equation, achieving optimal convergence rate O(h^{k+1}) and preserving charge conservation. Numerical experiments confirm the theory.
In this paper, we propose a conservative local discontinuous Galerkin method for one-dimensional nonlinear Schrödinger equation. By using special upwind-biased numerical fluxes, we establish the optimal rate of convergence $\mathcal O(h^{k+1})$, with polynomial of degree $k$ and grid size $h$. Meanwhile, we show that this method preserves the charge conservation law and thus we call it a conservative local discontinuous Galerkin method. Numerical experiments verify our theoretical result.