Optimal estimates on stabilized finite volume methods for the incompressible Navier–Stokes model in three dimensions

Abstract

Optimal estimates on stabilized finite volume methods for the three dimensional Navier–Stokes model are investigated and developed in this paper. Based on the global existence theorem [23], we first prove the global bound for the velocity in the H1‐norm in time of a solution for suitably small data, and uniqueness of a suitably small solution by contradiction. Then, a full set of estimates is then obtained by some classical Galerkin techniques based on the relationship between finite element methods and finite volume methods approximated by the lower order finite elements for the three dimensional Navier–Stokes model.