A posteriori error estimation and adaptivity based on VMS for the incompressible Navier–Stokes equations

In this work an explicit a posteriori error estimator for the steady incompressible Navier–Stokes equations is investigated. The error estimator is based on the variational multiscale theory, where the numerical solution is decomposed in resolved scales (FEM solution) and unresolved scales (FEM error). The error is estimated locally considering the residuals that emerge from the numerical solution and the error inverse-velocity scales, τ’s, associated with each type of residual. These error scales are provided in this paper, which have been computed a-priori solving a set of local problems with unit residuals. Therefore, the computational effort to predict the error is small and its implementation in any FEM code is simple. As an application, a strategy to develop adaptive meshes with the aim of optimizing the computational effort is shown. Numerical examples are presented to test the behavior of the error estimator.