Heid, Pascal; Praetorius, Dirk; Wihler, Thomas P. (2021). Energy contraction and optimal convergence of adaptive iterative linearized finite element methods. Computational methods in applied mathematics, 21(2), pp. 407-422. De Gruyter 10.1515/cmam-2021-0025
Full text not available from this repository. (Request a copy)We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [P. Heid and T. P. Wihler, Adaptive iterative linearization Galerkin methods for nonlinear problems, Math. Comp. 89 2020, 326, 2707–2734; P. Heid and T. P. Wihler, On the convergence of adaptive iterative linearized Galerkin methods, Calcolo 57 2020, Paper No. 24] satisfies an energy contraction property in the context of (abstract) strongly monotone problems. This property, in turn, is the crucial ingredient in the recent convergence analysis in [G. Gantner, A. Haberl, D. Praetorius and S. Schimanko, Rate optimality of adaptive finite element methods with respect to the overall computational costs, preprint 2020]. In particular, we deduce that adaptive iterative linearized finite element methods (AILFEMs) lead to full linear convergence with optimal algebraic rates with respect to the degrees of freedom as well as the total computational time.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Wihler, Thomas |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1609-4840 |
Publisher: |
De Gruyter |
Funders: |
[42] Schweizerischer Nationalfonds ; [UNSPECIFIED] Australian Science Fund ; [UNSPECIFIED] Australian Science Fund |
Projects: |
Projects 200021 not found. Projects 0 not found. Projects 0 not found. |
Language: |
English |
Submitter: |
Sebastiano Don |
Date Deposited: |
04 Feb 2022 15:19 |
Last Modified: |
05 Dec 2022 16:04 |
Publisher DOI: |
10.1515/cmam-2021-0025 |
URI: |
https://boris.unibe.ch/id/eprint/164660 |
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