On [H1]3×3, [H(curl)]3 and H(sym Curl) finite elements for matrix-valued Curl problems.
Saved in:
| Title: | On [H1]3×3, [H(curl)]3 and H(sym Curl) finite elements for matrix-valued Curl problems. |
|---|---|
| Authors: | Sky, Adam1 (AUTHOR) adam.sky@tu-dortmund.de, Muench, Ingo1 (AUTHOR), Neff, Patrizio2 (AUTHOR) |
| Source: | Journal of Engineering Mathematics. Oct2022, Vol. 136 Issue 1, p1-13. 13p. |
| Abstract: | In this work we test the numerical behaviour of matrix-valued fields approximated by finite element subspaces of [ H 1 ] 3 × 3 , [ H (curl) ] 3 and H (sym Curl) for a linear abstract variational problem connected to the relaxed micromorphic model. The formulation of the corresponding finite elements is introduced, followed by numerical benchmarks and our conclusions. The relaxed micromorphic continuum model reduces the continuity assumptions of the classical micromorphic model by replacing the full gradient of the microdistortion in the free energy functional with the Curl. This results in a larger solution space for the microdistortion, namely [ H (curl) ] 3 in place of the classical [ H 1 ] 3 × 3 . The continuity conditions on the microdistortion can be further weakened by taking only the symmetric part of the Curl. As shown in recent works, the new appropriate space for the microdistortion is then H (sym Curl) . The newly introduced space gives rise to a new differential complex for the relaxed micromorphic continuum theory. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Engineering Mathematics is the property of Springer Nature 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 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 159017375 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: On [H1]3×3, [H(curl)]3 and H(sym Curl) finite elements for matrix-valued Curl problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Sky%2C+Adam%22">Sky, Adam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> adam.sky@tu-dortmund.de</i><br /><searchLink fieldCode="AR" term="%22Muench%2C+Ingo%22">Muench, Ingo</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Neff%2C+Patrizio%22">Neff, Patrizio</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Engineering+Mathematics%22">Journal of Engineering Mathematics</searchLink>. Oct2022, Vol. 136 Issue 1, p1-13. 13p. – Name: Abstract Label: Abstract Group: Ab Data: In this work we test the numerical behaviour of matrix-valued fields approximated by finite element subspaces of [ H 1 ] 3 × 3 , [ H (curl) ] 3 and H (sym Curl) for a linear abstract variational problem connected to the relaxed micromorphic model. The formulation of the corresponding finite elements is introduced, followed by numerical benchmarks and our conclusions. The relaxed micromorphic continuum model reduces the continuity assumptions of the classical micromorphic model by replacing the full gradient of the microdistortion in the free energy functional with the Curl. This results in a larger solution space for the microdistortion, namely [ H (curl) ] 3 in place of the classical [ H 1 ] 3 × 3 . The continuity conditions on the microdistortion can be further weakened by taking only the symmetric part of the Curl. As shown in recent works, the new appropriate space for the microdistortion is then H (sym Curl) . The newly introduced space gives rise to a new differential complex for the relaxed micromorphic continuum theory. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Engineering Mathematics is the property of Springer Nature 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=159017375 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10665-022-10238-3 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1 Titles: – TitleFull: On [H1]3×3, [H(curl)]3 and H(sym Curl) finite elements for matrix-valued Curl problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Sky, Adam – PersonEntity: Name: NameFull: Muench, Ingo – PersonEntity: Name: NameFull: Neff, Patrizio IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2022 Type: published Y: 2022 Identifiers: – Type: issn-print Value: 00220833 Numbering: – Type: volume Value: 136 – Type: issue Value: 1 Titles: – TitleFull: Journal of Engineering Mathematics Type: main |
| ResultId | 1 |
