Finite volume method based on stabilized finite elements for the nonstationary Navier–Stokes problem

Abstract

Abstract A finite volume method based on stabilized finite element for the two‐dimensional nonstationary Navier–Stokes equations is investigated in this work. As in stabilized finite element method, macroelement condition is introduced for constructing the local stabilized formulation of the nonstationary Navier–Stokes equations. Moreover, for P 1 − P 0 element, the H 1 error estimate of optimal order for finite volume solution ( u h , p h ) is analyzed. And, a uniform H 1 error estimate of optimal order for finite volume solution ( u h , p h ) is also obtained if the uniqueness condition is satisfied. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007