椭圆问题的非协调Carey元逼近的误差估计中常数的精细估计(英文)  

Sharp Estimation of Interpolation Error Constants of a Nonconforming Carey Element Approximation for Second-order Elliptic Problems

作　　者：张亚东[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：《应用数学》2013年第4期725-731,共7页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (10971203,11271340)

摘　　要：本文主要研究在各向异性网格下非协调三角形Carey元逼近二阶椭圆问题,在抛弃传统有限元分析的必要工具Ritz投影算子的前提下,直接利用单元的插值性质,导出L2-模和H1-模意义下的最优阶误差估计中常数的精细估计.最后,给出一些数值结果验证了理论分析的正确性.In this paper, the famous nonconforming Carey triangular finite element is applied to approximate the second-order elliptic problem, by utilizing the properties of the interpolation on the element instead of the Ritz projection operator, which is an indispensable tool in the traditional finite element analysis, the sharp estimates of interpolation error constants for broken energy norm and L^2-norm on anisotropic triangular meshes are obtained. At last, some numerical results are provided to show the validity of the theoretical analysis.

关 键 词：Carey元 精细估计 插值误差 各向异性 

分 类 号：O242.21[理学—计算数学]