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W. Auzinger, H.J. Stetter:
"Defect corrections and multigrid iterations";
in: "`Multigrid Methods', Proceedings, Köln-Porz, Nov. 1981; Lecture Notes in Mathematics 960", Springer, Berlin, 1982.

At first we demonstrate how any defect correction iteration may be combined with an iterative procedure for its effective solution operator and derive a bound on the convergence factor for the combined iterative process. Then we consider the situation when the iterative solution procedure consists of multigrid cycles. Various implementation versions of a defect correction multigrid cycle are discussed, particularly for the case where defect correction is to achieve a higher order approximation to the differential equation. We also regard some algorithmic and quantitative details in the context of model problems. Finally we present some numerical examples.

http://www.math.tuwien.ac.at/~winfried/papers/article_DC_AND_MG_ITER.pdf