On basic iteration schemes for nonlinear AFC discretizations

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Date
2018
Volume
2533
Issue
Journal
Series Titel
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

Algebraic flux correction (AFC) finite element discretizations of steady-state convection-diffusionreaction 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.

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Keywords
Algebraic flux correction schemes, nonlinear discretizations, Kuzmin limiter, BJK limiter, fixed point iterations, formal Newton method
Citation
Jha, A., & John, V. (2018). On basic iteration schemes for nonlinear AFC discretizations (Vol. 2533). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2533
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