一维有限元后处理的EEP法的数学分析  

Mathematical Analysis of EEP Method for One-Dimensional Finite Element Postprocessing

作　　者：赵庆华[1] 周叔子[1] 朱起定[2] 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《应用数学和力学》2007年第4期401-405,共5页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10571046;10371038)

摘　　要：利用一维投影型插值与有限元超收敛基本估计,对一类两点边值问题,严格证明了袁驷等人由单元能量投影(EEP)法获得的节点恢复导数,当有限元空间的次数不超过4时,具有最佳阶超收敛.理论分析圆满地解释了已有的数值结果.For a class of two-point boundary value problems, by virtue of one-dimensional projection interpolation and finite element superconvergence fundamental estimations, it was proved that the nodal recovery derivative obtained by Yuan＇ s dement energy projection （EEP） method had the optimal order superconvergence on condition that the degree of finite element space is no more than 4. The theoretical analysis coincides with the reported numerical results.

关 键 词：超收敛应力 单元能量投影法 有限元 两点边值问题 投影型插值 

分 类 号：O242.21[理学—计算数学]