Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 671-688.
Published online: 2017-10
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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.
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.