TY - JOUR T1 - Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 671 EP - 688 PY - 2017 DA - 2017/10 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.y16008 UR - https://global-sci.org/intro/article_detail/nmtma/12364.html KW - AB -

This paper is concerned with numerical method for a two-dimensional time-dependent cubic nonlinear Schrödinger 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 $L^2$ error estimates for two fully discrete schemes by using elliptic projection operator. Finally, a numerical example is provided to verify our theoretical results.