Analysis of a finite volume element method for the Stokes problem

Alfio Quarteroni (1, 2) , Ricardo Ruiz Baier (2)

1 MOX - Modeling and Scientific Computing
2 CMCS - Modeling and Scientific Computing

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. The stabilization of the continuous lowest equal order pair finite volume discretization ($\mathbb{P}_1-\mathbb{P}_1$) is achieved by enriching the velocity space with bubble-like functions. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Mots clés: Stokes problem; multiscale stabilization; finite volume element method; a priori error estimates; superconvergence analysis

Domaines: Analyse numérique [math.NA]

Alfio Quarteroni, Ricardo Ruiz Baier. Analysis of a finite volume element method for the Stokes problem. Numerische Mathematik, 2011, pp.1. ⟨10.1007/s00211-011-0373-4⟩. ⟨hal-00462469v2⟩