A posteriori error estimators for the steady incompressible Navier-Stokes equations

Abstract

A residual-based a posteriori error estimator for finite element discretizations of the steady incompressible Navier{Stokes equations in the primitive variable formulation is discussed. Though the estimator is similar to existing ones, an alternate derivation is presented, involving an abstract estimate that may prove of some intrinsic value. The estimator is particularized to Hood{Taylor and modified Hood{Taylor finite elements and proved to be a global upper bound (up to a positive multiplicative constant) of the true error. Numerical examples are provided to illustrate the performance of the resulting mesh adaptation process. c 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 561{574, 1997