Superconvergence of the stable $$P_1-P_1$$ P 1 - P 1 finite element pair for Stokes problem

Abstract

We study the superconvergence of the stable lowest equal-order finite element pair solving the Stokes problem. The superclose property is proved for the interpolation function; then a superconvergence rate of $$O(h^{\frac{3}{2}})$$O(h32)-order is obtained for the velocity gradient approximation by using the post-processing technique, and an $$O(h^{\frac{3}{2}})$$O(h32)-order error estimate is derived for the pressure approximation. In addition, the asymptotically exact a posteriori error estimate also is given by means of the superconvergence result. Finally, some numerical experiments are provided to illustrate the theoretical analysis.