TY - JOUR
T1 - Superconvergence Analysis of Bilinear Finite Element for the Nonlinear Schrödinger Equation on the Rectangular Mesh
AU - Tian , Zhikun
AU - Chen , Yanping
AU - Wang , Jianyun
JO - Advances in Applied Mathematics and Mechanics
VL - 2
SP - 468
EP - 484
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2017-0156
UR - https://global-sci.org/intro/article_detail/aamm/12221.html
KW - Finite element method, nonlinear Schrödinger equation, superconvergence, interpolation post-processing.
AB - <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>