On the stability of collocated finite volume method for the generalized Stokes problem

In this paper, a symmetric stabilized collocated formulation of finite volume method is introduced and analyzed for the stationary generalized Stokes problem. This method is based on the lowest-order approximation using piecewise constant functions for both velocity and pressure unknowns. Stabilization is achieved by adding a discrete pressure term to the approximate formulation. The stability and convergence properties are established. Two numerical examples are presented to confirm the stability and accuracy of the proposed method.