广义神经传播方程新的非协调混合元方法的超逼近分析  

Superclose Estimates Analysis of a New Mixed Finite Elements Method for Generalized Nerve Conduction Equation

作　　者：张厚超[1] 毛凤梅[1] 白秀琴[1] 

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000

出　　处：《四川师范大学学报（自然科学版）》2017年第4期464-472,共9页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11271340);河南省科技计划项目(162300410082)

摘　　要：对一类非线性广义神经传播方程利用EQ_1^(rot)元及零阶Raviart-Thomas(R-T)元建立一个低阶非协调混合元格式.首先,证明逼近解的存在唯一性.其次,在半离散格式下,基于上述2个单元的高精度结果,借助EQ_1^(rot)元的特殊性质以及对时间t的导数转移技巧,导出原始变量u的H^1-模和中间变量p的L^2-模意义下O(h^2)阶的超逼近结果.最后,建立该方程的一个全离散逼近格式,分别得到原始变量u的H^1-模以及中间变量p的L^2-模意义下的具有O(h^2+τ~2)超逼近结果.这里,h和τ分别表示空间剖分参数及时间步长.Based on the nonconforming EQ1rotelement and the Raviart-Thomas （R-T） element, a new lower order nonconforming mixed finite elements method is proposed for Generalized nerve conduction equation. Firstly, the existence and uniqueness of approxi- mation solutions are proved. Secondly, based on the high accuracy results of the about two elements and derivative transferring tech- nique with respect to the time variable, the superclose with order O （ h2 ） for the primitive solution in H1 -norm and the intermediate vari- able p in L2-norm are obtained under semi-discrete scheme respectively. Finally, a new fully-discrete approximation scheme is proposed and the superclose estimates with order O（ h2 ＋τ2 ） are deduced for the primitive solution in H1 -norm and the intermediate variable p in L2-norm respectively. Here, h and ＂r are the subdivision parameter in space and time step respectively.

关 键 词：广义神经传播方程 非协调混合元方法 半离散及全离散格式 超逼近 

分 类 号：O242.21[理学—计算数学]