多套函数有限元逼近与拟协调板元

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Finite Element Approximations with Multiple Sets of Functions and Quasi-Conforming Elements for Plate Bending Problems

摘要: 继[1]、[2]的工作,本文根据多套函数有限元逼近的思想,建立了唐立民等人^[3]、[4]提出的拟协调板元的数学基础.

Abstract: Continuing refs. [1],[2]. we try toestablish here the mathematical foundation of quasi-conforming elements suggesied by Prof. Tang Limin and his colleagues for plate bending problems ^[3,4]. The main theme used in this paper is the finite element approximations with multiple sets of functions.

[1]	Zhang Hong-qing,The generalized patch test and 9-parameters quasi-conforming element,Proceedings of the Sino-France Symposium on Finite Element Methods,Edited by Feng Kang and J.L.Lions,Science Press,Gordon and Breach,Science Publishers,(1983),566-583.
[2]	张鸿庆,多套函数广义分片检验与12参数拟协调元,大连工学院学报,21, 3(1982), 11-19.
[3]	唐立民、陈万吉、刘迎曦,有限元分析中的拟协调元,大连工学院学报,19, 2(1980), 19-35
[4]	蒋和洋,用拟协调元法推导高精度三角形板弯曲单元,大连工学院学报,20,增刊2(1981).21-28.
[5]	钱伟长.《变分法与有限元》.上册.科学出版社.(1980).
[6]	Oden,J.T.,J.N.,Reddy,An Introdution to the Mathematical Theory of Finite Elements,Wiley-Interscience,New York(1976).
[7]	Stummel,F.,The generalized patch test,SIAM J.Num.Anal.16(1979),449-471.
[8]	Ciarlet,P.C.,The Finite Element Method for Elliptic Problems,North-Holland,Amsterdam,New York,Oxford,(1978).

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