Comparison results for the Stokes equations

This paper enfolds a medius analysis for the Stokes equations and compares different finite element methods (FEMs). A first result is a best approximation result for a P1P1 non-conforming FEM. The main comparison result is that the error of the P2P0P2P0-FEM is a lower bound to the error of the Bernardi–Raugel (or reduced P2P0P2P0) FEM, which is a lower bound to the error of the P1P1 non-conforming FEM, and this is a lower bound to the error of the MINI-FEM. The paper discusses the converse direction, as well as other methods such as the discontinuous Galerkin and pseudostress FEMs.Furthermore this paper provides counterexamples for equivalent convergence when different pressure approximations are considered. The mathematical arguments are various conforming companions as well as the discrete inf-sup condition.