An optimal order error estimate for an upwind discretization of the Navier—Stokes equations

Abstract

We analyze a finite-element approximation of the stationary incompressible Navier-Stokes equations in primitive variables. This approximation is based on the nonconforming P I/Po element pair of Crouzeix/Raviart and a special upwind discretization of the convective term. An optimal error estimate in a discrete HI-norm for the velocity and in the L'-norm for the pressure is proved. Some numerical results are presented. 0 1996 John Wiley & Sons, Inc.

An inf-sup Stable and Residual-Free Bubble Element for the Oseen Equations

“…We are interested in the case of small ν (high Reynolds numbers) in which numerical experiments show the need for stabilization [11,29,30]. In the next section, we will follow the concept of residual-free bubble stabilizations, which has been already successfully applied to scalar convection-diffusion equations [1,7,8,16].…”

Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations

“…We use a Samarskij upwinding stabilization analysed by Schieweck and Tobiska [10] for the non-conforming P 1 /P 0 -finite element discretization of the steady state Navier-Stokes equations.…”

A Finite Element Method for a Noncoercive Elliptic Problem with Neumann Boundary Conditions

“…Instead, we will show that for sufficiently small mesh sizes 0 < h h 0 the inf-sup constant β h > 0 of the discrete problem is uniformly bounded away from zero. In order to preserve the positivity ofû we discretize (1.1) by a combined finite-element finite-volume approach which has been already applied successfully for coercive convection-diffusion problems [1,2,3,11,13,15].…”