## 留言板

 引用本文: 梁国平, 傅子智. 混合杂交罚函数有限元方法及其应用[J]. 应用数学和力学, 1984, 5(3): 377-390.
Liang Guo-ping, Fu Zi-zhi. Mixed Hybrid Penalty Finite Element Method and Its Applications[J]. Applied Mathematics and Mechanics, 1984, 5(3): 377-390.
 Citation: Liang Guo-ping, Fu Zi-zhi. Mixed Hybrid Penalty Finite Element Method and Its Applications[J]. Applied Mathematics and Mechanics, 1984, 5(3): 377-390.

## Mixed Hybrid Penalty Finite Element Method and Its Applications

• 摘要: 对一般非协调有限元,目前采用最多的两种方法是罚函数法和混合、杂交法.前一种方法总能保证收敛,但精度差,条件数和稀疏性不好;后一种方法则要满足“秩条件”才能保证收敛,故单元的构造受到很大的限制.本文提出把这两种方法结合一起的有限元方法——混合杂交罚函数法.从理论上严格证明了(在非常一般的条件下)这种新方法总是收敛的,并且其精度、条件数以及稀疏性等皆与协调元相同,也就是说都是最优的. 最后应用这一方法具体构造了一个新的九自由度任意三角形弯板单元(每个顶点给三个自由度——一个位移和两个转角),其单元刚度矩阵计算公式与旧的九自由度三角形弯板单元的计算公式相差不多.但它对任意几何形状的平板都收敛于真解,如果真解u∈H3的话,它的三个弯矩具有一阶精度,位移及两个转角均具有二阶精度.
•  [1] (1)Babuska,I.and M.Zlamal,Nonconforming elements in finite element method with penalty,SIAM J.Numer,Anal.,Vol.10,No.5(1973). [2] (2) Feng Kang,On the theory of discontinuous finite element method,Journal of Computing Mathematics,1:4 (1979).(in Chinese). [3] (3) Fix,G.J.,G.Liang and D.H.Lee,Penalty-hybrid finite element method.(to be published in Math.and Comp.with Appl.). [4] (4) Brezzi,F.,On the ExisTence,Uniqueness and Approximation of Saddle Point Problems Arising from Lagragian Multipliers,RAIRO Numer.Anal.,8 R 2,(1974). [5] (5) Oden,J.T.and J.N.Reddy,Variational Methods in Theoretical Mechanics,Spring-Verlag,Heidelberg,(1976).,. [6] (6) Ciarlet,P.,The Finite Element Method for Elliptic Problems,North Holland Publisher,(1979). [7] (7) Oden,J.T.and J.N.Reddy,Mathematical Theory of Finite Elements,John Wiley & Sons,New York,(1975). [8] (8) Treves,F.,Basic Linear Partial Differential Equations,Academic Press,New York,(1975). [9] (9) Liang Guo-ping and Fu Zi-zhi,The construction of large elements in finite element method,Applied Math ematics and Mechanics,Vol.4,No.3,(1983). [10] (10) Kordratev,V.A.,Boundary Value Problems for Elliptic Equations in Domains with Conical or Singular Points,Trudy Moskov Mat.OBSC,16(1967).

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##### 出版历程
• 收稿日期:  1983-08-10
• 刊出日期:  1984-06-15

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