Applied Mathematics and Mechanics

, Volume 9, Issue 2, pp 135–142 | Cite as

On the embedding and compact properties of finite element spaces

  • Wang Ming
  • Zhang Hong-quing
Article

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.

Keywords

Element Space Basic Compactness Discontinuous Point Finite Element Approximation Finite Element Space 

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References

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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.MathSciNetCrossRefGoogle Scholar
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    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.Google Scholar
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    Stummel, F., Basic compactness properties of nonconforming and hybrid finite element spaces, RAIRO, Numer. Anal.,4, 1 (1980), 81–115.MathSciNetGoogle Scholar
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    Adams, R.A.,Sobolev Spaces, Academic Press, New York (1975).Google Scholar
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    Ciarlet, P.C.,The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, New York, Oxford (1978).Google Scholar

Copyright information

© SUT 1988

Authors and Affiliations

  • Wang Ming
    • 1
  • Zhang Hong-quing
    • 1
  1. 1.Dalian Institute of TechnologyInstitute of Applied MathematicsDalian

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