Adaptive Defect-Correction Methods for Viscous Incompressible Flow Problems

We consider a defect correction method (DCM) which has been used extensively in applications where solutions have sharp transition regions, such as high Reynolds number fluid flow problems. A reliable a posteriori error estimator is derived for a defect correction method. The estimator is further studied for two examples: (a) the case of a linear-diffusion, nonlinear convection-reaction equation, and (b) the nonlinear Navier–Stokes equations. Numerical experiments are provided which illustrate the utility of the resulting adaptive defect correction method for high Reynolds number, incompressible, viscous flow problems.