| Superconvergence analysis of bi-k-degree rectangular elements for two-dimensional time-dependent Schrödinger equation |
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| 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 |
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| 作者姓名： | Jianyun WANG Yanping CHEN |
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| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 11671157) |
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| 摘 要： |
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| 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 |
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| 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 |
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| Authors: | Jianyun Wang Yanping Chen |
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| 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 |
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| 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. |
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| Keywords: | coal infusion seepage flow permeation equation water infusiondestproof Schrödinger equation superconvergence elliptic projection interpolation post-processing |
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