A posteriori least-squares finite element error analysis for the Navier-Stokes equations

Abstract

A residual type a posteriori error estimator is presented for the least-squares finite element solution of stationary incompressible Navier-Stokes equations based on the velocity-vorticity-pressure formulation with nonstandard and standard boundary conditions. Using the coerciveness of the corresponding Stokes operator and the special feature of the nonlineariry of the formulation, it is shown that,the error estimator is exact for the Stokes problem and is asymptotically exact for the Navier-Stokes problem in an energy-like norm. The resulting adaptive method is highly parallel because it does not require to assemble the global, matrix and the error estimation can be completely localized without using any information from neighboring elements.