有限元空间的嵌入性质和紧致性
On the Embedding and Compact Properties of Finite Element Spaces
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摘要: 本文将Sobolev嵌入定理和Rellich-Kondrachov紧致定理推广到多套函数有限元空间.特殊地,在非协调元,杂交元和拟协调元空间等情形建立了这两个定理.Abstract: In this paper, the generalized Sobolev embedding theorem and the generalized Rellich-Kondrachov compact theorem for finite element spaces with multiple sets of functions are established. Specially, they are true for nonconforming, hybrid and quasi-conforming element spaces with certain conditions.
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[1] 张鸿庆、王鸣,拟协调元空间的紧致性和拟协调元法的收敛性,应用数学和力学,7, 5 (1988),409-423. [2] Zhang Hong-qing and Wang Ming, Finite element approximations with multiple sets of functions and quasi-conforming elements, Proc. of the 1984 Beijing Symposium on Differential Geometry and Differential Equations, Ed. Feng Kang, Science Press (1985), 354-365. [3] Stummel, F., Basic compactness properties of nonconforming and hybrid finite element spaces, RAIRO, Numer. Anal., 4, 1 (1980), 81-115. [4] Adams, R.A., Sobolev Spaces, Academic Press, New York (1975). [5] Ciarlet, P.C., The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, New York, Oxford (1978). -
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