带弱奇异核非线性积分微分方程的收敛性分析  

Convergence analysis for nonlinear integro-differential equations with a weakly singular kernel

作　　者：吴志勤[1] 石东伟[2] 

机构地区：[1]许昌学院数学与统计学院,河南许昌461000 [2]河南科技学院数学系,河南新乡453003

出　　处：《山东大学学报（理学版）》2012年第8期60-63,共4页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(10671184;10971203);高等学校博士学科点专项基金(20094101110006);国家自然科学基金数学天元基金(11026154)

摘　　要：利用双线性元对一类带弱奇异核非线性积分微分方程进行了研究。利用单元已有的高精度分析结果、借助投影算子和平均值技巧,在各向异性网格下得到了比以往文献高一阶的L2-模最优误差估计。The bilinear finite element approximate for a class of nonlinear integro-differential equations with weakly sin- gular kernel is studied. The optimal error estimate which is one order higher approximate than the results of the previous literature in L2-norm is derived for anisotropy meshes based on the known high accuracy analysis results of this element, the projection operator and the average skills mean-value.

关 键 词：积分微分方程 弱奇异核 各向异性 双线性元 最优误差估计 

分 类 号：O242.21[理学—计算数学]