| 两点边值问题的五次元有限体积法 |
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| 引用本文： | 王帅,左平,李永海.两点边值问题的五次元有限体积法[J].吉林大学学报(理学版),2010,48(4):521-528. |
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| 作者姓名： | 王帅 左平 李永海 |
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| 作者单位： | 1. 吉林大学 数学研究所, 长春 130012,2. 空军航空大学 基础部, 长春 130022;3. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 构造了求解两点边值问题的一种五次元Hermite型有限体积元法:试探函数空间取为五次有限元空间,其中的函数完全由节点上的函数值、一阶导数值和二阶导数值决定;检验函数空间取为相应于对偶剖分的分段二次函数空间.证明了误差的最优H1模收敛阶和L2模收敛阶估计,并给出了内部单元端点和中点的超收敛性结果.数值实验结果验证了方法的有效性.
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| 关 键 词： | 有限体积元法 试探函数空间 对偶剖分 检验函数空间 |
| 收稿时间： | 2009-12-17 |
Fifth-Order Finite Volume Element Methods for Two-Point Boundary Value Problems |
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| WANG Shuai,ZUO Ping,LI Yong-hai.Fifth-Order Finite Volume Element Methods for Two-Point Boundary Value Problems[J].Journal of Jilin University: Sci Ed,2010,48(4):521-528. |
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| Authors: | WANG Shuai ZUO Ping LI Yong-hai |
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| Institution: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China;2. Department of Foundation, Aviation University of Air Force, Changchun 130022, China;3. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | A fifth-order finite volume element scheme was constructed for two point boundary value problems, in which trial and test spaces werechosen as the fifth-order finite element space and the piecewise quadratic function space respectively. The optimal convergence rates in H1 and L2norm were proved, and the superconvergence of the scheme was obtained. The numerical examples confirm the theoretical results. |
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| Keywords: | finite volume element method trial function spaces dual partition test function spaces |
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