S. Prudhomme et Jt. Oden, A posteriori error estimation and error control for finite element approximations of the time-dependent Navier-Stokes equations, FINITE EL A, 33(4), 1999, pp. 247-262
We present an approach to estimate numerical errors in finite element appro
ximations of the time-dependent Navier-Stokes equations along with a strate
gy to control these errors. The error estimators and the error control proc
edure are based on the residuals of the Navier-Stokes equations, which are
shown to be comparable to error components in the velocity variable. The pr
esent methodology applies to the estimation of: numerical errors due to the
spatial discretization only. Its performance is demonstrated for two-dimen
sional:channel flows past a cylinder in the periodic regime. (C) 1999 Elsev
ier Science B.V. All rights reserved.