A modified Ka\v{c}anov iteration scheme with application to quasilinear diffusion models

Pascal Heid; Thomas P. Wihler

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arXiv · 2101.10137

A modified Ka\v{c}anov iteration scheme with application to quasilinear diffusion models

Pascal Heid·Thomas P. Wihler

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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.

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Pascal Heid, Thomas P. Wihler. 2021-01-25. A modified Ka\v{c}anov iteration scheme with application to quasilinear diffusion models. https://arxiv.org/abs/2101.10137

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