A posteriori error estimation of steady-state finite element solutions of the Navier-Stokes equations by a subdomain residual method

We present a subdomain residual method, as well as its mathematical basis, for estimating errors in steady-state finite element solutions of the incompressible Navier-Stokes equations. The estimated errors are obtained by solving a series of local problems in which velocity boundary condition is used wherever the exact traction boundary condition is not available. An iterative procedure similar to the Newton method is employed to improve the error estimates. The performance of the method is demonstrated in two numerical examples, i.e. the channel flow over a backward-facing step and past a circular cylinder at low Reynolds numbers.