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Adaptive defect-correction methods for viscous incompressible flow problems. (English) Zbl 1049.76038

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.

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
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