A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations

摘要

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