On the convergence of adaptive iterative linearized Galerkin methods

Heid, Pascal; Wihler, Thomas P. (2020). On the convergence of adaptive iterative linearized Galerkin methods. Calcolo, 57(3) Springer 10.1007/s10092-020-00368-4

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A wide variety of different (fixed-point) iterative methods for the solution of nonlinear equations exists. In this work we will revisit a unified iteration scheme in Hilbert spaces from our previous work [16] that covers some prominent procedures (including the Zarantonello, Kačanov and Newton iteration methods). In combination with appropriate discretization methods so-called (adaptive) iterative linearized Galerkin (ILG) schemes are obtained. The main purpose of this paper is the derivation of an abstract convergence theory for the unified ILG approach (based on general adaptive Galerkin discretization methods) proposed in [16]. The theoretical results will be tested and compared for the aforementioned three iterative linearization schemes in the context of adaptive finite element discretizations of strongly monotone stationary conservation laws.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Heid, Pascal and Wihler, Thomas

Subjects:

500 Science > 510 Mathematics

ISSN:

0008-0624

Publisher:

Springer

Funders:

[4] Swiss National Science Foundation

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

09 Feb 2021 13:34

Last Modified:

11 Mar 2021 20:20

Publisher DOI:

10.1007/s10092-020-00368-4

ArXiv ID:

1905.06682

Additional Information:

Paper No. 24, 23 pp

Uncontrolled Keywords:

Numerical solution methods for quasilinear elliptic PDE, Monotone problems, Fixed point iterations, Linearization schemes, Kačanov method · Newton method, Galerkin discretizations, Adaptive mesh refinement, Convergence of adaptive finite element methods

BORIS DOI:

10.48350/151248

URI:

https://boris.unibe.ch/id/eprint/151248

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