Abstract

In this paper, we propose a P1⊕RT0 - P0 discretization of the Stokes equations on general simplicial meshes in two/three dimension, which yields an exactly divergence-free and pressure independent velocity approximation with optimal order. The method has the following features. Firstly, the global number of the degrees of freedom of our method is the same as the low order Bernardi and Raugel (B-R) finite element method, while the number of the non-zero entries of the former is about half of the latter in the velocity-velocity region of the coefficient matrix. Secondly, our method can be easily transformed into a pressure-robust and stabilized P1-P0 discretization for the Stokes problem via the static condensation of the RT0 component. A priori error estimates and a posterior error estimate are obtained. Numerical experiments illustrate the robustness and accuracy of our method. Numerical methods based one the same idea for the N-S equations are under consideration.