The Construction of Large Elements in Finite Element Method

Liang Guo-ping; Fu Zi-zhi

Volume 4 Issue 3

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Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(3): 379-390

Liang Guo-ping, Fu Zi-zhi. The Construction of Large Elements in Finite Element Method[J]. Applied Mathematics and Mechanics, 1983, 4(3): 379-390.

Citation:

Liang Guo-ping, Fu Zi-zhi. The Construction of Large Elements in Finite Element Method[J]. Applied Mathematics and Mechanics, 1983, 4(3): 379-390.

Citation:

Liang Guo-ping, Fu Zi-zhi. The Construction of Large Elements in Finite Element Method[J]. Applied Mathematics and Mechanics, 1983, 4(3): 379-390.

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The Construction of Large Elements in Finite Element Method

Liang Guo-ping¹,
Fu Zi-zhi²

1.
Institute of Mathematics, Academic, Sinica, Beijing;
2.
Beijing Petroleum Design Institute, Beijing

Received Date: 1982-02-27
Publish Date: 1983-06-15

Abstract

Abstract

In the usual finite element method, the order of the interpolation in an element is kept unchanged, and the accuracy is raised by subdividing the grid denser and denser. Alternatively, in the large element method, the grid is kept unchanged, and the terms of approximate series in the element are increased to raise the accuracy.In this paper, a method for constructing large elements is presented. When using this method,two sets of variables, one set defined inside the element, and the other defined on the boundary of the element, are adopted. Then, these two sets of variables are combined by the hybrid-penalty function method.This method can be applied to any elliptic equations in a domain with arbitrary shape and arbitrary complex boundary condition.It is proved with strict mathematical method in this paper, that in general cases,the accuracy of this method is much higher than that of the usual element and the large element method presented in [7].Therefore,the degrees of freedom needed in this method are much fewer than those in the two methods if the same accuracy is preserved.

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References(10)

References

[1]	梁国平,分层解法——有限元的一个新算法,应用数学学报,2,1(1979).
[2]	梁国平,半解析法及其误差估计,计算数学,2, 3(1980)
[3]	Zienkiewicz,D.W.Kelly and P.Bettess,The coupling of the finite element method and boundary solution procedure,Int.J.Num.Method.Engng.,11,2,(1977).
[4]	梁国平、顾永耕,平面弹性断裂问题的半解析法,计算数学,1,4(1978).
[5]	Tong,P.and.T.H.H.Pian,A hybrid element approach to crack problems in plane elasticity,Int.J.Numer.Method.Eng.7,(1973),297-308.
[6]	李子才、粱国平,椭圆型方程边值问题的结合法,中国科学,(1981)
[7]	Babuska,I.,B.A.Szabo and L.N.Katz,The-version of the finite element method,SLAM J.Numer.Anal.,18:3,(1981).
[8]	Oden,J.T.and J.N.Reddy,Variational methods in theoretical mechanics,Springer-Verlag,Heidelberg,(1976).
[9]	Oden,J.T.and J.N.Reddy,Mathematical theory of finite elements,John Wiley & Sons,New York,(1976).
[10]	Treves,F.,Basic linear partial differential equations,Academic Press,New York,San Francisco,(1975).

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