On the Inf-Sup Stabillity of Crouzeix-Raviart Stokes Elements in 3D

  title={On the Inf-Sup Stabillity of Crouzeix-Raviart Stokes Elements in 3D},
  author={Stefan A. Sauter and C'eline Torres},
We consider non-conforming discretizations of the stationary Stokes equation in three spatial dimensions by Crouzeix-Raviart type elements. The original definition in the seminal paper by M. Crouzeix and P.-A. Raviart in 1973 is implicit and also contains substantial freedom for a concrete choice. In this paper, we introduce canonical Crouzeix-Raviart basis functions in 3D in analogy to the 2D case in a fully explicit way. We prove that this canonical Crouzeix-Raviart element for the Stokes… 

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