The inf-sup constant for Crouzeix-Raviart triangular elements of any polynomial order

04/04/2022

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by   S. Sauter, et al.

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In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of any polynomial order k≥1 on conforming triangulations and discontinuous pressure approximations of order k-1. We will bound the inf-sup constant from below independent of the mesh size and analyse its k-dependence. Our assumptions on the mesh are quite general, for odd k we require that the triangulations contain at least one inner vertex while for even k we assume that the triangulations consist of more than a single triangle.