@Article{NMTMA-10-671, author = {}, title = {Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {3}, pages = {671--688}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.y16008}, url = {http://global-sci.org/intro/article_detail/nmtma/12364.html} }