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

Abstract

In this paper, we consider the discretization of the two-dimensional stationary Stokes equation by Crouzeix-Raviart elements for the velocity of 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 show that it depends only logarithmically 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 for even k we assume that the triangulations consist of more than a single triangle.