Copyright © 2012 Zhe Yin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-order -error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.