Ervin, V. J.; Layton, W. J.; Maubach, J. M. Adaptive defect-correction methods for viscous incompressible flow problems. (English) Zbl 1049.76038 SIAM J. Numer. Anal. 37, No. 4, 1165-1185 (2000). Summary: 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. Cited in 32 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:defect correction; Navier-Stokes; finite element PDFBibTeX XMLCite \textit{V. J. Ervin} et al., SIAM J. Numer. Anal. 37, No. 4, 1165--1185 (2000; Zbl 1049.76038) Full Text: DOI