具有最佳超收敛阶的Galerkin有限元EEP法计算格式  

A SCHEME WITH OPTIMAL ORDER OF SUPER-CONVERGENCE BASED ON EEP METHOD FOR GALERKIN 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,结构工程与振动教育部重点实验室,北京100084

出　　处：《工程力学》2008年第11期1-7,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(50678093)

摘　　要：对二阶非自伴问题的一维Galerkin有限元法提出其后处理超收敛计算的EEP(单元能量投影)法改进的最佳超收敛计算格式,即用m次单元对足够光滑问题的Galerkin有限元解答,采用该格式计算的任一点的位移和应力都可以达到h2m阶的最佳超收敛结果。该文首先针对高次单元提出了凝聚试探形函数和凝聚检验形函数的概念,证明了相关的逼近定理和等价定理,然后给出了具体的算法公式。最后给出了一系列典型的数值算例用以验证这种最新的EEP法改进格式确实能够使位移和导数逐点达到最佳收敛阶。Based on the Element Energy Projection （EEP） method, the present paper presents, for one-dimensional C^0 Galerkin FEM （Finite Element Method）, an improved scheme with an optimal order of super-convergence, i.e. for elements of degree m with sufficiently smooth solutions, the proposed scheme is capable of producing O（h^2m） super-convergence for both displacements and stresses at any point on any element in post-processing stage. To achieve that, condensed trial shape functions and condensed test shape functions were developed first, and then associated theorems of approximation and equivalence were proved. Based on these theorems, the formulation of the proposed scheme was obtained. Finally a series of typical numerical examples were given, which indicate that this improved scheme can really achieve the optimal order of super-convergence at any point of the solution domain.

关 键 词：GALERKIN有限元 一维问题 超收敛 最佳收敛阶 单元能量投影 

分 类 号：TU318[建筑科学—结构工程]