AN A POSTERIORI ERROR ESTIMATE FOR FINITE-ELEMENT APPROXIMATIONS OF THE NAVIER-STOKES EQUATIONS

In this paper, an a posteriori error estimate for the steady state Nav ier-Stokes equations, based on element residual methods, is developed. Here, a special norm is designed to measure the error in velocity and pressure for incompressible flow problems. We prove that under mild a ssumptions, the new norm is, asymptotically, equivalent to the product space norm for the Navier-Stokes equations; moreover, by summing the solutions of local elliptic residual problems, the computed global err or is shown to be always bounded below by the true global error when m easured in the new norm. A numerical experiment on the backstep channe l problem is given to demonstrate the effectiveness of the error estim ate.