@Article{NMTMA-10-671,
author = {Jianyun Wang and Yunqing Huang},
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 = {<p style="text-align: justify;">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.&nbsp;We prove optimal&nbsp;$L^2$ error estimates for two fully discrete schemes by using elliptic projection operator.
Finally, a numerical example is provided to verify our theoretical results.<br/></p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.y16008},
url = {http://global-sci.org/intro/article_detail/nmtma/12364.html}
}