A posteriori error estimations for mixed finite-element approximations to the Navier-Stokes equations
This provides a practical framework for error estimation in nonlinear evolutionary Navier-Stokes simulations, benefiting computational fluid dynamics practitioners.
The authors derive a posteriori error estimates for mixed finite element discretizations of the Navier-Stokes equations, reducing the error estimation for the evolutionary problem to that of a steady Stokes problem, and validate with numerical experiments.
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.