Defect-correction multigrid methods for nonlinear problems

摘要

Auzinger and Stetter [1] combine a multigrid method with defect-correction iteration and derive a composite iterative procedure which they call the DCMG (defect-correction multigrid) cycle. Using a high-order discrete operator in the coarsegrid correction and a lower-order operator in relaxation, the DCMG cycle achieves the higher-order approximation [4]. In an analogous way, DCMG can be used to solve nonlinear PDEs by using the nonlinear operator in correction and a related linear operator in relaxation. We prove convergence of such a DCMG scheme and give an error estimation.