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Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation
引用本文:Jianyun WANG,Yanping CHEN. Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation[J]. 应用数学和力学(英文版), 2018, 39(9): 1353-1372. DOI: 10.1007/s10483-018-2369-9
作者姓名:Jianyun WANG  Yanping CHEN
基金项目:Project supported by the National Natural Science Foundation of China (No. 11671157)
摘    要:

关 键 词:coal infusion  seepage flow  permeation equation  water infusiondestproof  Schrödinger equation  elliptic projection  superconvergence  interpolation post-processing  
收稿时间:2017-12-13

Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation
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. DOI: 10.1007/s10483-018-2369-9
Authors:Jianyun Wang  Yanping Chen
Affiliation: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
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(hk+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(hk+1 + τ2) in the H1 norm can be obtained in the Crank-Nicolson fully discrete scheme.
Keywords:coal infusion  seepage flow  permeation equation  water infusiondestproof  Schrödinger equation  superconvergence  elliptic projection  interpolation post-processing  
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