Superconvergence of tricubic block finite elements  

作　　者：LIU JingHong SUN HaiNa ZHU QiDing 

机构地区：[1]Department of Fundamental Courses,Ningbo Institute of Technology,Zhejiang University,Ningbo 315100,China [2]School of Mathematics and Computer Science,Hunan Normal University,Changsha 410081,China

出　　处：《Science China Mathematics》2009年第5期959-972,共14页中国科学：数学（英文版）

基　　金：supported by Natural Science Foundation of Ningbo City (Grant No. 2008A610020);National Natural Science Foundation of China (Grant No. 10671065);the Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 07C576, 03C212)

摘　　要：In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green's function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.In this paper, we first introduce interpolation operator of projection type in three dimensions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution u h and the tricubic interpolant of projection type Π h 3 u have superclose gradient in the pointwise sense of the L ∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.

关 键 词：block finite element interpolation operator of projection type SUPERCONVERGENCE SUPERCLOSENESS weak estimate discrete derivative Green’s function 65N30 

分 类 号：O241.82[理学—计算数学]