Adaptive fixed point iterations for semilinear elliptic partial differential equations

Amrein, Mario

doi:10.1007/s10092-019-0321-8

Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-17873

Publication type:	Article in scientific journal
Type of review:	Peer review (publication)
Title:	Adaptive fixed point iterations for semilinear elliptic partial differential equations
Authors:	Amrein, Mario
et. al:	No
DOI:	10.1007/s10092-019-0321-8 10.21256/zhaw-17873
Published in:	Calcolo
Volume(Issue):	56
Issue:	3
Page(s):	30
Issue Date:	2019
Publisher / Ed. Institution:	Springer
ISSN:	0008-0624 1126-5434
Language:	English
Subjects:	Adaptive fixed point method; A posteriori error analysis; Strongly monotone problem; Semilinear elliptic problem
Subject (DDC):	510: Mathematics
Abstract:	In this paper we study the behaviour of finite dimensional fixed point iterations, induced by discretization of a continuous fixed point iteration defined within a Banach space setting. We show that the difference between the discrete sequence and its continuous analogue can be bounded in terms depending on the discretization of the infinite dimensional space and the contraction factor, defined by the continuous iteration. Furthermore, we show that the comparison between the finite dimensional and the continuous fixed point iteration naturally paves the way towards a general a posteriori error analysis that can be used within the framework of a fully adaptive solution procedure. In order to demonstrate our approach, we use the Galerkin approximation of singularly perturbed semilinear monotone problems. Our scheme combines the fixed point iteration with an adaptive finite element discretization procedure (based on a robust a posteriori error analysis), thereby leading to a fully adaptive fixed-point-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach.
Further description:	Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)
URI:	https://digitalcollection.zhaw.ch/handle/11475/17873
Fulltext version:	Published version
License (according to publishing contract):	Licence according to publishing contract
Restricted until:	2024-08-31
Departement:	School of Management and Law
Organisational Unit:	Institute for Risk & Insurance (IRI)
Appears in collections:	Publikationen School of Management and Law

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Amrein, M. (2019). Adaptive fixed point iterations for semilinear elliptic partial differential equations. Calcolo, 56(3), 30. https://doi.org/10.1007/s10092-019-0321-8

Amrein, M. (2019) ‘Adaptive fixed point iterations for semilinear elliptic partial differential equations’, Calcolo, 56(3), p. 30. Available at: https://doi.org/10.1007/s10092-019-0321-8.

M. Amrein, “Adaptive fixed point iterations for semilinear elliptic partial differential equations,” Calcolo, vol. 56, no. 3, p. 30, 2019, doi: 10.1007/s10092-019-0321-8.

AMREIN, Mario, 2019. Adaptive fixed point iterations for semilinear elliptic partial differential equations. Calcolo. 2019. Bd. 56, Nr. 3, S. 30. DOI 10.1007/s10092-019-0321-8

Amrein, Mario. 2019. “Adaptive Fixed Point Iterations for Semilinear Elliptic Partial Differential Equations.” Calcolo 56 (3): 30. https://doi.org/10.1007/s10092-019-0321-8.

Amrein, Mario. “Adaptive Fixed Point Iterations for Semilinear Elliptic Partial Differential Equations.” Calcolo, vol. 56, no. 3, 2019, p. 30, https://doi.org/10.1007/s10092-019-0321-8.