摘要
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(hk+1)in the H1norm 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(hk+1+ τ2) in the H1norm can be obtained in the Crank-Nicolson fully discrete scheme.
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.
基金
Project supported by the National Natural Science Foundation of China(No.11671157)
作者简介
Corresponding author,E-mail:yanpingchen@scnu.edu.cn
