三角形线元与二次元L^2投影的整体超收敛  

GLOBAL SUPERCONVERGENCE FOR L^2-PROJECTION TO LINEAR AND QUADRATIC TRIANGULAR ELEMENTS

作　　者：陈传淼[1] 

机构地区：[1]湖南师范大学计算所,长沙410081

出　　处：《计算数学》2003年第4期385-392,共8页Mathematica Numerica Sinica

基　　金：国家重点基础研究计划(批准号19990328004);国家自然科学基金(No.19331021)

摘　　要：1.引言 设Ω是多角形域,Γ0是边界Γ的角点集,三角剖分是均匀的.记m次有限元空间为Shm,u及v∈Shm可满足下列边界条件之一: BV1.在Γ上,u=v=0; BV2.对任何u,在Γ上v自由.Based on an orthogonal expansion in a triangle, superconvergence for L2-projection to linear and quadratic triangular elements is studied. Assume that Ω is a polygonal domain, triangulation is uniform and Th is a set of all vertexes and side midpoints. Then, on Th, the average gradient D(u-uh)-O(h2) for linear element Uh, and u-uh = O(h4) for quadratic element uh. Under some boundary conditions, these properties upto the boundary are valid.

关 键 词：三角形线元 二次元 L^2投影算子 整体超收敛 插值算子 椭圆投影算子 有限元分析 三角剖分 

分 类 号：O241.82[理学—计算数学]