DEFECT CORRECTION WITH A FULLY COUPLED INEXACT NEWTON METHOD

Abstract

We examine the characteristics of a fully coupled inexact Newton method using defect correction to obtain high-order solutions for two problems: natural convection in a square cavity and mixed-convection flow over 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 discretization used for the residuals. Defect correction employs low-order operators for the Jacobian but high-order operators for the residuals. We employ an O(h³) convection operator in the residual vector and upwinding in the Jacobian. We find that defect correction is an efficient and effective way to achieve high-order solutions.