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Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-17873
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dc.contributor.authorAmrein, Mario-
dc.date.accessioned2019-08-08T09:04:17Z-
dc.date.available2019-08-08T09:04:17Z-
dc.date.issued2019-
dc.identifier.issn0008-0624de_CH
dc.identifier.issn1126-5434de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/17873-
dc.descriptionErworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)de_CH
dc.description.abstractIn 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.de_CH
dc.language.isoende_CH
dc.publisherSpringerde_CH
dc.relation.ispartofCalcolode_CH
dc.rightsLicence according to publishing contractde_CH
dc.subjectAdaptive fixed point methodde_CH
dc.subjectA posteriori error analysisde_CH
dc.subjectStrongly monotone problemde_CH
dc.subjectSemilinear elliptic problemde_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleAdaptive fixed point iterations for semilinear elliptic partial differential equationsde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Management and Lawde_CH
zhaw.organisationalunitInstitut für Risk & Insurance (IRI)de_CH
dc.identifier.doi10.1007/s10092-019-0321-8de_CH
dc.identifier.doi10.21256/zhaw-17873-
zhaw.funding.euNode_CH
zhaw.issue3de_CH
zhaw.originated.zhawYesde_CH
zhaw.pages.start30de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume56de_CH
zhaw.embargo.end2024-08-31de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
zhaw.author.additionalNode_CH
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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.


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