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In this paper, we consider the discretization of the two-dimensionalstationary Stokes equation by Crouzeix-Raviart elements for the velocity ofpolynomial order $k\geq1$ on conforming triangulations and discontinuouspressure approximations of order $k-1$. We will bound the inf-sup constant frombelow independent of the mesh size and show that it depends onlylogarithmically on $k$. Our assumptions on the mesh are very mild: for odd $k$we require that the triangulations contain at least one inner vertex while foreven $k$ we assume that the triangulations consist of more than a singletriangle.

The inf-sup constant for $hp$-Crouzeix-Raviart triangular elements