@Article{AAMM-14-3,
author = {Wang, Jianyun and Zhikun, Tian},
title = {Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {14},
number = {3},
pages = {652--665},
abstract = {<p style="text-align: justify;">The superconvergence of a two-dimensional time-independent nonlinear
Schrödinger equation are analyzed with the rectangular Lagrange type finite element of order $k$. Firstly, the error estimate and superclose property are given in $H^1$-norm
with order $\mathcal{O}(h^{k+1})$ between the finite element solution $u_h$ and the interpolation function $u_I$ by use of the elliptic projection operator. Then, the global superconvergence is
obtained by the interpolation post-processing technique. In addition, some numerical
examples with the order $k = 1$ and $k = 2$ are provided to demonstrate the theoretical
analysis.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2020-0268},
url = {https://global-sci.com/article/72915/superconvergence-of-finite-element-approximations-of-the-two-dimensional-cubic-nonlinear-schrodinger-equation}
}