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

摘要

A 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.