Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

doi:10.1007/s10483-018-2369-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (9): 1353-1372.doi: https://doi.org/10.1007/s10483-018-2369-9

• 论文 • 上一篇

Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

Jianyun WANG¹, Yanping CHEN²

1. School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan Province, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

收稿日期:2017-12-13 修回日期:2018-04-20 出版日期:2018-09-01 发布日期:2018-09-01
通讯作者: Yanping CHEN E-mail:yanpingchen@scnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11671157)

Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

Jianyun WANG¹, Yanping CHEN²

1. School of Science, Hunan University of Technology, Zhuzhou 412007, Hunan Province, China;
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received:2017-12-13 Revised:2018-04-20 Online:2018-09-01 Published:2018-09-01
Contact: Yanping CHEN E-mail:yanpingchen@scnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11671157)

摘要/Abstract

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 Schrödinger equation with the finite element method. The error estimate and superconvergence property with order O(h^k+1) in the H¹ 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 + τ²) in the H¹ norm can be obtained in the Crank-Nicolson fully discrete scheme.

关键词: coal infusion, seepage flow, permeation equation, water infusiondestproof, Schrödinger equation, elliptic projection, superconvergence, interpolation post-processing

Abstract: 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 Schrödinger equation with the finite element method. The error estimate and superconvergence property with order O(h^k+1) in the H¹ 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 + τ²) in the H¹ norm can be obtained in the Crank-Nicolson fully discrete scheme.

Key words: coal infusion, seepage flow, permeation equation, water infusiondestproof, Schrödinger equation, superconvergence, elliptic projection, interpolation post-processing

中图分类号:

Jianyun WANG, Yanping CHEN. Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(9): 1353-1372.

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Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation

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