固端法:二维有限元先验定量误差估计与控制  

FIXED-END METHOD:A PRIORI QUANTITATIVE ERROR ESTIMATE AND CONTROL FOR TWO-DIMENSIONAL FEM

作　　者：袁驷[1] 袁全 YUAN Si;YUAN Quan(Department of Civil Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学土木工程系,北京100084

出　　处：《工程力学》2021年第1期8-14,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(51878383,51378293)。

摘　　要：该文基于有限元超收敛计算的单元能量投影(Element Energy Projection,简称EEP)法,尝试将一维有限元中新近提出的先验定量误差估计的“固端法”拓展到二维有限元分析,以Poisson方程为例,用EEP公式预先估算出各单元的误差,可以不经有限元求解计算而直接给出满足精度要求的网格划分。该文给出的初步数值算例验证了该法的有效性。Based on the element energy projection(EEP)method for super-convergence calculation,this paper attempts to extend the recently proposed‘fixed-end method’,a priori quantitative error estimate for onedimensional finite element method(FEM),to two-dimensional(2D)FEM.In this approach,the EEP method is used to estimate the errors a priori on each individual 2D element and a desirable mesh can be accordingly generated immediately without the need for obtaining FE solutions in advance.Taking the Poisson equation as the model problem,some initial numerical results are given to show the validity and effectiveness of the proposed technique.

关 键 词：二维有限元法 单元能量投影 固端法 先验定量估计 自适应网格划分 

分 类 号：O302[理学—力学]