| Lagrange三次有限体积元法的超收敛现象 |
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| 引用本文： | 丁玉琼,左平.Lagrange三次有限体积元法的超收敛现象[J].吉林大学学报(理学版),2011,49(2):159-163. |
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| 作者姓名： | 丁玉琼 左平 |
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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 |
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| 摘 要： | 基于三角形网上求解Poisson方程的Lagrange三次有限体积元法, 给出了超收敛性的数值结果. 数值实验表明, 在三角形单元的对称点(即3边中点和3个角顶点)上, 数值解平均梯度的收敛阶约为4阶, 比按H1模的收敛阶(O(h3))约高一阶.
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| 关 键 词： | 有限体积元法 Lagrange三次元 对偶剖分 超收敛 |
| 收稿时间： | 2010-08-31 |
Superconvergence Phenomenon for Lagrange Cubic Finite Volume Element Method |
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| DING Yu-qiong,ZUO Ping.Superconvergence Phenomenon for Lagrange Cubic Finite Volume Element Method[J].Journal of Jilin University: Sci Ed,2011,49(2):159-163. |
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| Authors: | DING Yu-qiong ZUO Ping |
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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 |
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| Abstract: | Based on the Lagrangian cubic element finite volume method for Poisson equation on triangular meshes constructed by us,we found that the convergence rate of average gradient of the numerical solutions is approximately 4 order at the symmetrical points of triangular element(i.e.midpoints of three edges and three vertices) through the numerical experiments,which is nearly one order higher than that of the H1 norm(O(h3)). |
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| Keywords: | finite volume element method Lagrange cubic basis dual partition superconvergence |
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