Optimal error estimate of conservative local discontinuous Galerkin method for nonlinear Schrödinger equation

In this paper, we propose a conservative local discontinuous Galerkin method for a one-dimensional nonlinear Schrödinger equation. By using special generalized alternating numerical fluxes, we establish the optimal rate of convergence O(hk+1), with polynomial of degree k and grid size h. Meanwhile, we show that this method preserves the charge conservation law. Numerical experiments verify our theoretical result.