Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schr(o)dinger Equation

摘要

This paper is concemed with numerical method for a two-dimensional timedependent cubic nonlinear Schr(o)dinger equation.The approximations are obtained by the Galerkin finite element method in space in conjunction with the backward Euler method and the Crank-Nicolson method in time,respectively.We prove optimal L2 error estimates for two fully discrete schemes by using elliptic projection operator.Finally,a numerical example is provided to verify our theoretical results.