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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Zhang Hong-qing and Wang Ming, On the compactness of quasi-conforming element spaces and the convergence of quasi-conformingelement method,Appl. Math. Mech.,7, 5 (1986), 443–459.
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.
Stummel, F., Basic compactness properties of nonconforming and hybrid finite element spaces, RAIRO, Numer. Anal.,4, 1 (1980), 81–115.
Adams, R.A.,Sobolev Spaces, Academic Press, New York (1975).
Ciarlet, P.C.,The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, New York, Oxford (1978).
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Ming, W., Hong-quing, Z. On the embedding and compact properties of finite element spaces. Appl Math Mech 9, 135–142 (1988). https://doi.org/10.1007/BF02456009
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DOI: https://doi.org/10.1007/BF02456009