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

@article{Sauter2022OnTI, title={On the Inf-Sup Stabillity of Crouzeix-Raviart Stokes Elements in 3D}, author={Stefan A. Sauter and C'eline Torres}, journal={ArXiv}, year={2022}, volume={abs/2205.00062} }

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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