An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids.
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| Title: | An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids. |
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| Authors: | Heid, Pascal1 (AUTHOR) pascal.heid@maths.ox.ac.uk, Süli, Endre1 (AUTHOR) endre.suli@maths.ox.ac.uk |
| Source: | Applied Numerical Mathematics. Nov2022, Vol. 181, p364-387. 24p. |
| Subjects: | Incompressible flow, Fluid flow, Finite element method, Fluids, Rheology |
| Abstract: | In this work, we further extend the theory in [ C. Kreuzer, E. Süli, Adaptive finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology, ESAIM: Math. Model. Numer. Anal. 50 (5) (2016) 1333–1369] on the adaptive finite element analysis of implicitly constituted incompressible fluid flow problems by taking into account the approximation of the nonlinear finite element solutions by an iterative solver. Thereby we show that the computable sequence generated by the modified algorithm still has a weak limit point, which is a solution of the given problem. Our abstract theory can be applied to Bingham fluids, both with and without the convective term. The performance of the adaptive iterative linearised finite element algorithm in this context is illustrated by two numerical experiments. [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 158605578 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Heid%2C+Pascal%22">Heid, Pascal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pascal.heid@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Süli%2C+Endre%22">Süli, Endre</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> endre.suli@maths.ox.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Nov2022, Vol. 181, p364-387. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Incompressible+flow%22">Incompressible flow</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+flow%22">Fluid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Fluids%22">Fluids</searchLink><br /><searchLink fieldCode="DE" term="%22Rheology%22">Rheology</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this work, we further extend the theory in [ C. Kreuzer, E. Süli, Adaptive finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology, ESAIM: Math. Model. Numer. Anal. 50 (5) (2016) 1333–1369] on the adaptive finite element analysis of implicitly constituted incompressible fluid flow problems by taking into account the approximation of the nonlinear finite element solutions by an iterative solver. Thereby we show that the computable sequence generated by the modified algorithm still has a weak limit point, which is a solution of the given problem. Our abstract theory can be applied to Bingham fluids, both with and without the convective term. The performance of the adaptive iterative linearised finite element algorithm in this context is illustrated by two numerical experiments. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.apnum.2022.06.011 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: 364 Subjects: – SubjectFull: Incompressible flow Type: general – SubjectFull: Fluid flow Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Fluids Type: general – SubjectFull: Rheology Type: general Titles: – TitleFull: An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Heid, Pascal – PersonEntity: Name: NameFull: Süli, Endre IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2022 Type: published Y: 2022 Identifiers: – Type: issn-print Value: 01689274 Numbering: – Type: volume Value: 181 Titles: – TitleFull: Applied Numerical Mathematics Type: main |
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