Transport-stabilized semidiscretizations of the incompressible Navier-Stokes equation

Within the framework of finite element methods, the paper investigates a general approximation technique for the nonlinear convective term of Navier-Stokes equations. The approach is based on an upwind method of the finite volume type. It has been proved that the discrete convective term satisfies the well-known collection of sufficient conditions for convergence of the finite element solution. For a particular nonconforming scheme, the assumptions have been verified in detail and the estimate of the semidiscrete velocity error has been proved.