Adaptive Defect-Correction Methods for Viscous Incompressible Flow Problems

Abstract

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.