广义神经传播方程最低阶新混合元格式的高精度分析

doi:10.6040/j.issn.1671-9352.0.2014.410

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (08): 78-89.doi: 10.6040/j.issn.1671-9352.0.2014.410

广义神经传播方程最低阶新混合元格式的高精度分析

樊明智¹, 王芬玲¹, 石东洋²

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

收稿日期:2014-09-16 出版日期:2015-08-20 发布日期:2015-07-31
作者简介:樊明智(1969- ), 男, 硕士, 教授, 研究方向为有限元方法及应用研究. E-mail:mathfanmz@163.com
基金资助:
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)

High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations

FAN Ming-zhi¹, WANG Fen-ling¹, SHI Dong-yang²

1. School of Mathematics and Statistics, Xuchang University, Xuchang 461000, Henan, China;
2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, China

Received:2014-09-16 Online:2015-08-20 Published:2015-07-31

摘要/Abstract

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

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.

Key words: superclose properties and superconvergence results, new mixed element, the generalized nerve conductive equations, semi-discrete and fully-discrete schemes

中图分类号:

O242.21

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(08): 78-89.

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(NATURAL SCIENCE), 2015, 50(08): 78-89.

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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

High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations

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