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

作　　者：樊明智[1] 王芬玲[1] 石东洋[2] 

机构地区：[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

出　　处：《山东大学学报（理学版）》2015年第8期78-89,共12页Journal of Shandong University(Natural Science)

基　　金：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Nédélec's元,对广义神经传播方程建立了最低阶自然满足Brezzi-Babuska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。A lowest order new mixed element approximate scheme with the bi!inear element and Nede1eccs element for the generalized nerve conductive equations is proposed, which can satisfy Brezzi-Babu^ka condition automatically. Based on high accuracy analysis of the mixed element and interpolation post-processing technique, the superclose prop- erties and superconvergence results of original variable in H^1-nonn 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 H^1 -norm and in- termediate variable in L2-norm are separately derived.

关 键 词：广义神经传播方程 超逼近性和超收敛结果 新混合元 半离散和全离散格式 

分 类 号：O242.21[理学—计算数学]