Adaptive defect correction methods for convection dominated, convection diffusion problems

We present a posteriori error estimates for a defect correction method for approximating solutions of convection diffusion problems. The algorithms and estimators include the possibility of using in the discretization a nonlinear selection mechanism, which we find, improves solution quality in and near layers. Energy norm and L2 a posteriori error estimates are proven for the full algorithm. Two examples of fully adaptive finite element-defect correction calculations are presented. These examples illustrate the scheme and demonstrate the effectiveness of the method.