On basic iteration schemes for nonlinear AFC discretizations
- Jha, Abhinav
- John, Volker
2010 Mathematics Subject Classification
- 65N22 65N30
- Algebraic flux correction schemes, nonlinear discretizations, Kuzmin limiter, BJK limiter, fixed point iterations, formal Newton method
Algebraic flux correction (AFC) finite element discretizations of steady-state convection-diffusion-reaction equations lead to a nonlinear problem. This paper presents first steps of a systematic study of solvers for these problems. Two basic fixed point iterations and a formal Newton method are considered. It turns out that the fixed point iterations behave often quite differently. Using a sparse direct solver for the linear problems, one of them exploits the fact that only one matrix factorization is needed to become very efficient in the case of convergence. For the behavior of the formal Newton method, a clear picture is not yet obtained.
- Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018, G.N. Barrenechea, J. Mackenzie, eds., vol. 135 of Lecture Notes in Computational Science and Engineering, Springer, Cham, 2020, pp. 113--128, DOI https://doi.org/10.1007/978-3-030-41800-7_7 .