Optimal Error Estimates of Conservative Local Discontinuous Galerkin Method for Nonlinear Schr'odinger Equation

摘要

In this paper, we propose a conservative local discontinuous Galerkin methodfor one-dimensional nonlinear Schr\"odinger equation. By using specialupwind-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 andthus we call it a conservative local discontinuous Galerkin method. Numericalexperiments verify our theoretical result.