A modified Ka\v{c}anov iteration scheme with application to quasilinear diffusion models
Abstract
The classical Ka\v{c}anov scheme for the solution of nonlinear variational problems can be interpreted as a fixed point iteration method that updates a given approximation by solving a linear problem in each step. Based on this observation, we introduce a modified Ka\v{c}anov method, which allows for (adaptive) damping, and, thereby, to derive a new convergence analysis under more general assumptions and for a wider range of applications. For instance, in the specific context of quasilinear diffusion models, our new approach does no longer require a standard monotonicity condition on the nonlinear diffusion coefficient to hold. Moreover, we propose two different adaptive strategies for the practical selection of the damping parameters involved.
Cite
@article{arxiv.2101.10137,
title = {A modified Ka\v{c}anov iteration scheme with application to quasilinear diffusion models},
author = {Pascal Heid and Thomas P. Wihler},
journal= {arXiv preprint arXiv:2101.10137},
year = {2021}
}