DEFECT CORRECTION WITH A FULLY COUPLED INEXACT NEWTON METHOD

We examine the characteristics of a fully coupled inexact Newton metho d using defect correction to obtain high-order solutions for two probl ems: natural convection in a square cavity and mired-convection flow o ver a backward step. Newton's method produces a linearized system with a Jacobian matrix and a residual vector, each of which can be formed using different discrete operators. Solution accuracy depends on the d iscretization used for the residuals. Defect correction employs low-or der operators for the Jacobian bat high-order operators for the residu als. We employ an O(h(3)) convection operator in the residual vector a nd upwinding in the Jacobian. We find that defect correction is an eff icient and effective way to achieve high-order solutions.