六维线性与张量积k(k≥1)次有限元的超收敛  

Superconvergence of the six-dimensional linear and tensorproduct k(k≥1)-order finite elements

作　　者：刘经洪[1] 朱起定[2] 贾银锁[3] 

机构地区：[1]浙江大学宁波理工学院公共基础部,宁波315100 [2]湖南师范大学数学与计算机科学学院,长沙410081 [3]上饶师范学院数学与计算机科学学院,上饶334001

出　　处：《中国科学：数学》2015年第8期1337-1344,共8页Scientia Sinica：Mathematica

基　　金：浙江省自然科学基金(批准号:LY13A010007);宁波市自然科学基金(批准号:2013A610104);国家自然科学基金(批准号:11161039)资助项目

摘　　要：本文研究六维椭圆问题线性与张量积k(k≥1)次有限元的超收敛性.首先介绍离散导数δ函数、L^2投影算子、正则导数Green函数和离散导数Green函数的概念,然后利用权范数估计导出离散导数Green函数的W^(1,1)半范估计,最后利用第一型弱估计和离散导数Green函数的估计获得线性与张量积k(k≥1)次有限元的导数的逐点超收敛估计.In this paper, we study superconvergence of the linear and tensor-product k （k ≥ 1）-order finite elements for the six-dimensional elliptic problem. First, the definitions of the discrete derivative 5 function, L2-projection operator, generalized derivative Green＇s funciton, and discrete derivative Green＇s function are in- troduced. Second, the Wl＇l-seminorm estimate for the discrete derivative Green＇s function is derived by using the weighted-norm estimates. Finally, with the weak estimate of the first type and the estimate for the discrete deriva- tive Green＇s function, pointwise superconvergent estimates for the derivatives of the linear and tensor-product k （k≥ 1）-order finite elements are obtained.

关 键 词：离散导数 Green 函数 六维有限元 弱估计 超收敛 

分 类 号：O241.82[理学—计算数学]