2022/04/04 by Sauter, S. · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2204.01270
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.