On an efficient solution strategy of Newton type for implicit finite element schemes based on algebraic flux correction

Abstract

AbstractA discrete Newton approach is applied to implicit flux‐limiting schemes based on the concept of algebraic flux correction. The Jacobian matrix is approximated by divided differences and assembled edge by edge. The use of a nodal flux limiter leads to an extended stencil which can be constructed a priori. Numerical examples for 2D benchmark problems are presented to compare the performance of the algebraic Newton method with the defect correction approach. Copyright © 2007 John Wiley & Sons, Ltd.