Defect correction for the advection-diffusion equation Original Research Article

A defect correction method for the advection-diffusion equation is presented. The discretization is performed by 2nd order finite difference schemes (β-schemes) where the 2nd order upstream scheme is combined with the standard central scheme. For preconditioning the usual first order upstream scheme is employed. The defect correction iteration is used for relaxation inside a multigrid procedure. It is shown that the smoothing analysis yields rather pessimistic results with rates of about 0.7–0.8. In the practical computation the discretization error is reached in 2 V-cycles. Numerical results are presented which demonstrate the high efficiency of our treatment.