| 一维Lagrange四次元有限体积法的超收敛性 |
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| 引用本文： | 李莎莎,左平.一维Lagrange四次元有限体积法的超收敛性[J].吉林大学学报(理学版),2012,50(3):397-403. |
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| 作者姓名： | 李莎莎 左平 |
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| 作者单位： | 1. 吉林大学 数学研究所, 长春 130012,2. 大庆师范学院 数学科学学院, 黑龙江 大庆 163712;3. 空军航空大学 基础部, 长春 130022 |
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| 基金项目： | 黑龙江省青年自然科学基金，大庆师范学院青年基金 |
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| 摘 要： | 通过取等距节点四次Lagrange插值的导数超收敛点作为对偶单元的节点, 取Lagrange型四次有限元空间为试探函数空间, 取相应于对偶剖分的分片常数函数空间为检验函数空间的方法, 得到了求解两点边值问题的四次元有限体积法, 证明了该方法具有最优的H1模和L2模误差估计, 并讨论了对偶单元节点的导数超收敛估计. 数值实验验证了理论分析结果.
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| 关 键 词： | 两点边值问题 四次有限体积元法 导数超收敛点 误差估计 |
| 收稿时间： | 2011-11-16 |
Superconvergence of One Dimension Lagrange Fourth-Order Finite Volume Element Method |
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| LI Sha-sha
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ZUO Ping.Superconvergence of One Dimension Lagrange Fourth-Order Finite Volume Element Method[J].Journal of Jilin University: Sci Ed,2012,50(3):397-403. |
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| Authors: | LI Sha-sha ZUO Ping |
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| Institution: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China;2. Department of Mathematics, Daqing Normol University, Daqing 163712, Heilongjiang Province, China;3. Department of Foundation, Aviation University of Air Force, Changchun 130022, China |
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| Abstract: | We chose fourth order Lagrange interpolated function associated with the nodes as trial function,piecewise constant function as test function,and derivative superconvergent points as dual partition nodes so that a new kind of Lagrange fourth order finite volume element method was obtained for solving two-point boundary value problems.It was proved that the method has optimal H1 and L2 error estimates.The superconvergence of numerical derivatives was discussed.Finally,the numerical experiments show the results of theoretical analysis. |
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| Keywords: | two-point boundary value problem fourth order finite volume element method derivative superconvergent point error estimate |
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