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https://doi.org/10.21256/zhaw-17873| Publikationstyp: | Beitrag in wissenschaftlicher Zeitschrift |
| Art der Begutachtung: | Peer review (Publikation) |
| Titel: | Adaptive fixed point iterations for semilinear elliptic partial differential equations |
| Autor/-in: | Amrein, Mario |
| et. al: | No |
| DOI: | 10.1007/s10092-019-0321-8 10.21256/zhaw-17873 |
| Erschienen in: | Calcolo |
| Band(Heft): | 56 |
| Heft: | 3 |
| Seite(n): | 30 |
| Erscheinungsdatum: | 2019 |
| Verlag / Hrsg. Institution: | Springer |
| ISSN: | 0008-0624 1126-5434 |
| Sprache: | Englisch |
| Schlagwörter: | Adaptive fixed point method; A posteriori error analysis; Strongly monotone problem; Semilinear elliptic problem |
| Fachgebiet (DDC): | 510: Mathematik |
| Zusammenfassung: | 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. |
| Weitere Angaben: | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) |
| URI: | https://digitalcollection.zhaw.ch/handle/11475/17873 |
| Volltext Version: | Publizierte Version |
| Lizenz (gemäss Verlagsvertrag): | Lizenz gemäss Verlagsvertrag |
| Gesperrt bis: | 2024-08-31 |
| Departement: | School of Management and Law |
| Organisationseinheit: | Institut für Risk & Insurance (IRI) |
| Enthalten in den Sammlungen: | Publikationen School of Management and Law |
Dateien zu dieser Ressource:
| Datei | Beschreibung | Größe | Format | |
|---|---|---|---|---|
| Amrein2019_Article_AdaptiveFixedPointIterationsFo.pdf Bis 2024-08-31 | 875.95 kB | Adobe PDF | Öffnen/Anzeigen |
Zur Langanzeige
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.
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