带弱奇异核非线性积分微分方程的有限元分析  

Finite Element Analysis for Nonlinear Integro Differential Equation with Weakly Singular Kernel

作　　者：樊明智[1] 王芬玲[1] 牛裕琪[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]郑州大学数学系,河南郑州450052

出　　处：《数学的实践与认识》2012年第12期141-149,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10971203);高等学校博士学科点专项科研基金(20094101110006);河南省教育厅自然科学基金(2010A110018;12A110021)

摘　　要：讨论了带弱奇异核的非线性抛物积分微分方程的Hermite型各向异性矩形元逼近.在各向异性网格下导出了关于Riesz投影的L^2和H^1模的误差估计.在半离散和向后欧拉全离散格式下,基于Riesz投影的性质并利用平均值技巧,分别得到了L^2模意义下的最优误差估计.An Hermite-type anisotropic rectangular element approximation is discussed for nonlinear parabolic integro-differential equation with a weakly singular kernel. Error estimates in L2 and H1 norms of Riesz projection are derived on the anisotropic meshes. Based on the properties of Riesz projection, the optimal order error estimates in L^2 norm are gained by use of mean-value technique under semi-discrete and backward Euler fully-discrete schemes, respectively.

关 键 词：带弱奇异核的非线性抛物积分微分方程 Hermite型各向异性矩形元 最优误差估计 半离散和全离散格式 

分 类 号：O241.82[理学—计算数学]