拟协调元空间的紧致性和拟协调元法的收敛性
On the Compactness of Quasi-Conforming Element Spaces and the Convergence of Quasi-Conforming Element Method
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摘要: 本文首先讨论拟协调元空间的紧致性,把Rellich紧致定理推广到拟协调元空间序列,进而把广义Poincare、Friedrichs和Poincare-Friedrichs等不等式推广到拟协调元空间.然后讨论拟协调元法的收敛性和误差估计.本文证明了如果拟协调元空间具有逼近性和强连续性、满足单元秩条件且通过检验IPT,则近似解是收敛的.做为例子,我们证明了6参、9参、12参、15参、18参及21参拟协调元的收敛精度在L2,2(Ω)范数下分别是O(hτ)、O(hτ)、O(hτ2)、O(hτ2)、O(hτ3)及O(hτ4)量级.Abstract: In this paper,the compactness of quasi-conforming clement spices and the convergence of quasi-conforming element method are discussed.The well-known rellich compactness theorem is generalized to the sequences of quasi-conforming element spaces with certain properties,and the generalized poincare inequality,the generalized Friedrichs inequality and the generalzed inequality of Poincare-Friedrichs are proved true for them.The error estimates are also given.It is shown that the quasi-conforming element method is convergent if the quasi-conforming element spaces have the approximability and the strong continuity,and satisfy the rank condition of element and pass test IPT.As practical examples,6-parameter,9-parameter,12-parameter,15-parameter,18-parameter and 21-parameter quasi-conforming elements are shown to be convergent,and tlieir.L2,2(Ω)-errors are O(hτ)、O(hτ)、O(hτ2)、O(hτ2)、O(hτ3)and O(hτ4)respectively.
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[1] 张鸿庆、王鸣,多套函数育限元逼近与拟协调板元,应用数学与力学,6,1(1985),41-52. [2] Zhang Hongqing,Wang Ming,Finite element approximations with multiple sets of functions and quasi-conforming elements,第五次国际双微会议(DD5)论文集,北京(1984). [3] 唐立民、陈万言、刘迎曦,有限元分析中的拟协调元,大连工学院学报,19,2(1980)16-35. [4] 陈万吉、刘迎曦、唐立民,拟协调元列式,大连工学院学学报,19,2(1980). [5] 蒋和洋,用拟协调元方法推导高精度-二角形板弯曲单元,大连上学院学报,20,增刊2(1981)21-28. [6] Stummel,F.,The generalized patch test,SIAM J.Num.Anal.16(1971).449-471. [7] 冯康,沦间断有限元的理论,计算数学,1,4(1979)378-385. [8] Stummel,F.,Basic compactness properties of nonconforming and hybrid finite element spaces,RAIRO,Anahse,Sumeriqe,Numerieal Analresis,4,1(1980),81-115. [9] Ciarlet,P,C.,The Finite Element Method for Elliptic Problems,North-Holland,Amsterdam,New York,Oxford(1978). [10] 吉田耕作,《泛函分析》(吴元恺等译),人民教育出版社(l980) -
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