Lp error estimate of nonlinear Schrödinger equation using a two‐grid finite element method

Abstract

AbstractA two‐grid finite element scheme is presented for nonlinear Schrödinger equation. superconvergence error estimates of finite element solutions based on bound of finite element solutions is proved. The optimal order error estimations of the two‐grid solution in the and norm are given without any time‐step size conditions. It is shown, both theoretically and numerically, that the coarse space can be extremely coarse, with no loss in the order of accuracy.