Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics.
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| Title: | Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics. |
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| Authors: | Erkmen, Dilek1,2 (AUTHOR) derkmen@mtu.edu, Labovsky, Alexander E.1 (AUTHOR) aelabovs@mtu.edu |
| Source: | Applied Mathematics & Computation. May2019, Vol. 349, p48-52. 5p. |
| Subjects: | Magnetohydrodynamics, Algorithms, Finite element method, Mathematics theorems, Mathematical decoupling |
| Abstract: | Abstract An algorithm for resolving magnetohydrodynamic (MHD) flows has been presented recently, that allows for a stable decoupling of the system and uses the penalty-projection method for extra efficiency. The algorithm relies on the choice of Scott–Vogelius finite elements to complement the grad-div stabilization. We propose a small modification of the algorithm, which allows for its usage even with the less sophisticated (and more computationally attractive) Taylor–Hood pair of finite element spaces. We demonstrate numerically, that the new modification of the method is first order accurate in time (as expected by the theory), while the existing method would fail on the Taylor–Hood finite elements (the blow-up of the solution is demonstrated). [ABSTRACT FROM AUTHOR] |
| Copyright of Applied Mathematics & Computation 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: 134354936 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Erkmen%2C+Dilek%22">Erkmen, Dilek</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> derkmen@mtu.edu</i><br /><searchLink fieldCode="AR" term="%22Labovsky%2C+Alexander+E%2E%22">Labovsky, Alexander E.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> aelabovs@mtu.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Applied+Mathematics+%26+Computation%22">Applied Mathematics & Computation</searchLink>. May2019, Vol. 349, p48-52. 5p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Magnetohydrodynamics%22">Magnetohydrodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+theorems%22">Mathematics theorems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+decoupling%22">Mathematical decoupling</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract An algorithm for resolving magnetohydrodynamic (MHD) flows has been presented recently, that allows for a stable decoupling of the system and uses the penalty-projection method for extra efficiency. The algorithm relies on the choice of Scott–Vogelius finite elements to complement the grad-div stabilization. We propose a small modification of the algorithm, which allows for its usage even with the less sophisticated (and more computationally attractive) Taylor–Hood pair of finite element spaces. We demonstrate numerically, that the new modification of the method is first order accurate in time (as expected by the theory), while the existing method would fail on the Taylor–Hood finite elements (the blow-up of the solution is demonstrated). [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Applied Mathematics & Computation 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.amc.2018.12.036 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 5 StartPage: 48 Subjects: – SubjectFull: Magnetohydrodynamics Type: general – SubjectFull: Algorithms Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Mathematics theorems Type: general – SubjectFull: Mathematical decoupling Type: general Titles: – TitleFull: Note on the usage of grad-div stabilization for the penalty-projection algorithm in magnetohydrodynamics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Erkmen, Dilek – PersonEntity: Name: NameFull: Labovsky, Alexander E. IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 05 Text: May2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 00963003 Numbering: – Type: volume Value: 349 Titles: – TitleFull: Applied Mathematics & Computation Type: main |
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