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| 广义神经传播方程最低阶新混合元格式的高精度分析 | |
| 引用本文： | 樊明智,王芬玲,石东洋. 广义神经传播方程最低阶新混合元格式的高精度分析[J]. 山东大学学报(理学版), 2015, 50(8): 78-89. DOI: 10.6040/j.issn.1671-9352.0.2014.410 |
| 作者姓名： | 樊明智 王芬玲 石东洋 |
| 作者单位： | 1. 许昌学院数学与统计学院, 河南 许昌 461000; 2. 郑州大学数学与统计学院, 河南 郑州 450001 |
| 基金项目： | 国家自然科学基金(11271340); 河南省教育厅自然科学基金项目(14A110009);许昌市科技局项目(1404009) |
| 摘 要： | 利用双线性元和Nédéle?s元,对广义神经传播方程建立了最低阶自然满足Brezzi-Babuška条件的新混合元逼近格式.基于该混合元的高精度分析和插值后处理算子技术,在半离散格式下分别导出了原始变量的H1模及中间变量的L2模的超逼近性质和整体超收敛结果.当f(u)=f(X)时建立了一个具有二阶精度的全离散逼近格式,分别得到了原始变量的H1模的超逼近性和中间变量的L2模的最优误差估计. |
| 关 键 词： | 半离散和全离散格式 超逼近性和超收敛结果 广义神经传播方程 新混合元 |
| 收稿时间： | 2014-09-16 |
High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations |
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| FAN Ming-zhi,WANG Fen-ling,SHI Dong-yang. High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations[J]. Journal of Shandong University, 2015, 50(8): 78-89. DOI: 10.6040/j.issn.1671-9352.0.2014.410 | |
| Authors: | FAN Ming-zhi WANG Fen-ling SHI Dong-yang |
| Affiliation: | 1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China; 2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China |
| Abstract: | A lowest order new mixed element approximate scheme with the bilinear element and Nédélec?s element for the generalized nerve conductive equations is proposed, which can satisfy Brezzi-Babuška condition automatically. Based on high accuracy analysis of the mixed element and interpolation post-processing technique, the superclose properties and superconvergence results of original variable in H1-norm and intermediate variable in L2-norm are deduced separately for semi-discrete scheme. At the same time, a second order fully-discrete scheme when is f(u) equal to f(X) is established and the superclose properties and the optimal order error estimates of original variable in H1-norm and intermediate variable in L2-norm are separately derived. |
| Keywords: | superclose properties and superconvergence results new mixed element the generalized nerve conductive equations semi-discrete and fully-discrete schemes |
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