一维C^1有限元EEP超收敛位移计算简约格式的误差估计  

AN ERROR ESTIMATE OF EEP SUPER-CONVERGENT DISPLACEMENT OF SIMPLIFIED FORM IN ONE-DIMENSIONAL C^1 FEM

作　　者：袁驷[1] 邢沁妍[1] 叶康生[1] 

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：《工程力学》2015年第9期16-19,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(51378293,51078199);清华大学自主科研计划项目(2011THZ03)

摘　　要：该文对一维C1有限元后处理超收敛计算的EEP(单元能量投影)法简约格式中的位移解给出误差估计的数学证明,即对足够光滑问题的m(>3)次单元的有限元解答,采用EEP法简约格式得到的单元内任一点位移超收敛解均可以达到hm+2的收敛阶,比常规有限元位移解的收敛阶至少高一阶。For one-dimensional C^1 problems of the Ritz Finite Element Method （FEM）, an error estimate of the super-convergent displacement is presented for the simplified form of the Element Energy Projection （EEP） method used for super-convergence computation in post-processing stage of FEM. The mathematical analysis proves that for elements of degree m（〉3） with sufficiently smooth problems and solutions, EEP displacement of the simplified form is capable of producing a convergence order of h^m＋2 at any point on an element, i.e. being at least one order higher than the displacement from conventional FEM.

关 键 词：C1有限元 一维问题 超收敛 收敛阶 单元能量投影 

分 类 号：TU318[建筑科学—结构工程]