Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem

The aim of this paper is to develop and analyze a family of stabilized discontinuous finite volume element methods for the Stokes equations in two and three spatial dimensions. The proposed scheme is constructed using a baseline finite element approximation of velocity and pressure by discontinuous piecewise linear elements, where an interior penalty stabilization is applied. A priori error estimates are derived for the velocity and pressure in the energy norm, and convergence rates are predicted for velocity in the $$L^2$$L2-norm under the assumption that the source term is locally in $$ H^1$$H1. Several numerical experiments in two and three spatial dimensions are presented to validate our theoretical findings.