Superconvergence of Finite Element Approximations of the Two-Dimensional Cubic Nonlinear Schrödinger Equation
Year: 2022
Author: Jianyun Wang, Zhikun Tian
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 3 : pp. 652–665
Abstract
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 H1-norm with order O(hk+1) between the finite element solution uh and the interpolation function uI 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2020-0268
Advances in Applied Mathematics and Mechanics, Vol. 14 (2022), Iss. 3 : pp. 652–665
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Superconvergence nonlinear Schrödinger equation finite element method elliptic projection.