@Article{AAMM-10-468,
author = {Tian , ZhikunChen , Yanping and Wang , Jianyun},
title = {Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrödinger Equation on the Rectangular Mesh},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2018},
volume = {10},
number = {2},
pages = {468--484},
abstract = {<p style="text-align: justify;">In this paper, we investigate the superconvergence property of a time-dependent nonlinear Schrödinger equation with the bilinear finite element method on the rectangular mesh. We prove the superclose error estimate in $H^1$-norm with order $\mathcal{O}(h^2)$ between the approximated solution and the elliptic projection of the exact solution. Moreover, we obtain the global superconvergence result in $H^1$-norm with order $\mathcal{O}(h^2)$ by the interpolation post-processing operator.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2017-0156},
url = {http://global-sci.org/intro/article_detail/aamm/12221.html}
}