一维有限元的EEP单元及其自适应分析  

EEP Elements for the 1D Finite Element Method and the Adaptivity Analysis

作　　者：杨帅[1] 袁驷[1] YANG Shuai;YUAN Si(Key Laboratory of Civil Engineering Safety and Durability,Ministry of Education,Department of Civil Engineering,Tsinghua University,Beijing 100084,P.R.China)

机构地区：[1]清华大学土木工程系土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《应用数学和力学》2025年第1期1-11,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51878383,51378293)。

摘　　要：对m(>1)次单元,基于单元能量投影(element energy projection,简称EEP)法提出的简约格式位移解u∗具有比常规有限元解uh至少高一阶的精度,据此提出了EEP单元概念,并给出以EEP单元作为最终解的自适应有限元求解策略.通过编制相应的计算程序分析了一维非自伴随问题,计算结果与理论预期吻合较好,验证了自适应求解策略的有效性和可靠性.研究结果表明:该法可以给出按最大模度量、逐点满足误差限的解答,相较于常规单元,最终的求解单元数更少.For the elements of degree m(>1),simplified form solution u∗based on the element energy projection(EEP)method has at least 1-order higher accuracy than conventional finite element solution uh.As a result,the EEP element,with simplified form EEP solution u∗in as the final solution,was proposed,and a corresponding adaptive finite element analysis strategy for EEP elements was developed.By means of the developed algorithm,the 1D 2-point boundary value problem was analyzed,and the computation results are in good agreement with theoretical solutions,verifying the effectiveness and reliability of the proposed adaptivity strategy.The theoretical study and numerical experiments show that,the proposed method provides an EEP element solution satisfying the preset error tolerances in the maximum norm with fewer elements and less adaptive steps compared to conventional finite elements.

关 键 词：一维有限元 单元能量投影(EEP) EEP单元 自适应有限元法 

分 类 号：O342[理学—固体力学]