广义神经传播方程非协调类Wilson元的超收敛分析及外推  

Superconvergence Analysis and Extrapolations of Nonconforming Quasi-Wilson Element to the Generalized Nerve Conductive Equations

作　　者：王萍莉[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：《生物数学学报》2013年第4期672-680,共9页Journal of Biomathematics

基　　金：国家自然科学基金(10971203;11101381);教育部高等学校博士学科点专项科研基金(20094101110006);国家天元基金(11026154);河南省自然科学基金(2010A110018;2011A110020)

摘　　要：在半离散格式下研究了广义神经传播方程的非协调类Wilson有限元方法.利用该单元相容误差比协调误差高一阶的特殊性质和双线性元的高精度分析技巧,得到了相应的超逼近性质和超收敛结果.进一步地,构造了一个新的外推格式,并借助于该单元相容误差比协调误差高两阶的特殊性质,由此导出了能量模意义下具有O(h^3)阶的外推效果.Nonconforming Quasi-Wilson finite element for the Generalized Nerve Conduc- tive Equations is discussed under semi-discrete scheme. By use of the special property, which the consistency error is one order higher than that of the interpolation error, and high accucy results of the bilinear finite element, the superclose property and the superconvergence result are obtained. Furthermore, a new extrapolation sheme is proposed, based on the consistency error is two order higher than that of the interpolation error, the three order extrapolation result is derNed under Hi-norm.

关 键 词：广义神经传播方程 类WILSON元 超收敛 外推 

分 类 号：O242.21[理学—计算数学]