| 解一维抛物方程的基于应力佳点的二次有限体积元法 |
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| 引用本文： | 孙佳慧,秦丹丹,于长华.解一维抛物方程的基于应力佳点的二次有限体积元法[J].吉林大学学报(理学版),2011,49(4):643-651. |
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| 作者姓名： | 孙佳慧 秦丹丹 于长华 |
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| 作者单位： | 1. 空军航空大学 基础部, 长春 130022,2. 吉林大学 数学研究所, 长春 130012 |
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| 摘 要： | 构造了求解一维抛物问题的一种新的Lagrange型二次全离散有限体积元法, 取应力佳点作为对偶单元的节点, 试探函数空间取Lagrange型二次有限元空间, 检验函数空间取分片常数函数空间. 证明了新方法具有最优阶的H1模和L2模误差估计, 并讨论了H1模的整体超收敛估计及在应力佳点导数的逐点超收敛估计. 数值实验验证了理论分析结果.
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| 关 键 词： | 抛物方程 应力佳点 误差估计 二次有限体积元法 |
| 收稿时间： | 2010-09-25 |
Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems |
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| SUN Jia-hui,QIN Dan-dan,YU Chang-hua.Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems[J].Journal of Jilin University: Sci Ed,2011,49(4):643-651. |
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| Authors: | SUN Jia-hui QIN Dan-dan YU Chang-hua |
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| Institution: | 1. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;2. Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | A new Lagrangian quadratic finite volume element method based on optimal stress points was presented for solving
one dimensional parabolic problems with trial and test spaces as the Lagrangian quadratic finite element space and the piecewise constant function space respectively. It is proved that the method has optimal order H1 and L2error estimates. In addition, we discussed the global superconvergence in H1 norm and the locally pointwise superconvergence of numerical derivatives at optimal stress points. The numerical experiment confirms the results of theoretical analysis. |
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| Keywords: | quadratic finite volume element methods parabolic equations optimal stress points error estimate |
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