Heid, Pascal; Wihler, Thomas P. (2022). A modified Kačanov iteration scheme with application to quasilinear diffusion models. ESAIM: Mathematical modelling and numerical analysis (ESAIM: M2AN), 56(2), pp. 433-450. EDP Sciences 10.1051/m2an/2022008
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The classical Kačanov 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 Kačanov 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.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Wihler, Thomas |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
2822-7840 |
Publisher: |
EDP Sciences |
Language: |
English |
Submitter: |
Zarif Ibragimov |
Date Deposited: |
21 Feb 2023 08:01 |
Last Modified: |
21 Feb 2023 23:27 |
Publisher DOI: |
10.1051/m2an/2022008 |
BORIS DOI: |
10.48350/178968 |
URI: |
https://boris.unibe.ch/id/eprint/178968 |
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