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《应用数学和力学(英文版)》 2018-09
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Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schr?dinger equation

Jianyun WANG;Yanping CHEN;School of Science, Hunan University of Technology;School of Mathematical Sciences, South China Normal University;  
Superconvergence has been studied for long, and many different numerical methods have been analyzed. This paper is concerned with the problem of superconvergence for a two-dimensional time-dependent linear Schr?dinger equation with the finite element method. The error estimate and superconvergence property with order O(h~(k+1))in the H~1 norm are given by using the elliptic projection operator in the semi-discrete scheme. The global superconvergence is derived by the interpolation post-processing technique. The superconvergence result with order O(h~(k+1)+ τ~2) in the H~1 norm can be obtained in the Crank-Nicolson fully discrete scheme.
【Fund】: Project supported by the National Natural Science Foundation of China(No.11671157)
【CateGory Index】: O241.8
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