一类非线性拟双曲方程Hermite型有限元分析  

Hermite Type Finite Element Analysis for a Class of Nonlinear Qusi-hyperbolic Equations

作　　者：梁洪亮[1] 乔保民[1] 

机构地区：[1]商丘师范学院数学系,河南商丘476000

出　　处：《河南科技大学学报（自然科学版）》2011年第6期84-89,10,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：河南省自然科学基金项目(092300410148);河南省教育厅自然科学研究基金项目(2011A110013)

摘　　要：利用有限元方法研究一类广泛的非线性广义神经传播方程。首先,讨论其在半离散格式下解的收敛性;其次,利用插值算子与R itz-Volterra投影相一致的特殊性质得到了解的超逼近性质;最后,通过构造一个插值后处理算子导出了解的整体超收敛结果。In this paper,the generalized nonlinear nerve conductive equations were discussed by using finite element.Firstly,the convergence about the solution of these equations was obtained.Secondly,the result of superclose of the solution could be acquired by virtue of the property that the interpolation operator was accordant with the Ritz-Volterra projection.Finally,based on the interpolated postprocessing technique,the global superconvergence of the solution was derived.

关 键 词：广义神经传播方程 Hermite元 半离散 超收敛 

分 类 号：O242.21[理学—计算数学]