A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations. (arXiv:1011.2878v1 [math.NA])

A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations. (arXiv:1011.2878v1 [math.NA]): "

A posteriori estimates for mixed finite element discretizations of the
Navier-Stokes equations are derived. We show that the task of estimating the
error in the evolutionary Navier-Stokes equations can be reduced to the
estimation of the error in a steady Stokes problem. As a consequence, any
available procedure to estimate the error in a Stokes problem can be used to
estimate the error in the nonlinear evolutionary problem. A practical procedure
to estimate the error based on the so-called postprocessed approximation is
also considered. Both the semidiscrete (in space) and the fully discrete cases
are analyzed. Some numerical experiments are provided.

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