Analysis of a finite volume element method for the Stokes problem

作者：Quarteroni Alfio; Ruiz Baier Ricardo^*

来源：Numerische Mathematik, 2011, 118(4): 737-764.

DOI：10.1007/s00211-011-0373-4

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

• 出版日期2011-8