Superconvergence of the Finite Volume Method for Stokes Problems

Abstract

This paper presents a superconvergence analysis of the finite volume method for Stokes problems using the $P_1$ – $P_1$ velocity-pressure element pair. Based on some superclose estimates on the interpolation function, we derive a superconvergence result of rate $\mathcal{O}(h^{\frac{3}{2}})$ for the post-processed velocity approximation in the $H^1$-norm and for the directly computed pressure approximation in the $L_2$-norm, respectively. Numerical experiments are provided to illustrate the theoretical analysis.