TY - JOUR
T1 - Fully Discrete Galerkin Finite Element Method for the Cubic Nonlinear Schrödinger Equation
AU - Jianyun Wang & Yunqing Huang
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 - <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>