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Novel [formula omitted]-conforming finite elements for the relaxed micromorphic sequence.

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Title: Novel [formula omitted]-conforming finite elements for the relaxed micromorphic sequence.
Authors: Sky, Adam1 (AUTHOR) adam.sky@uni.lu, Neunteufel, Michael2 (AUTHOR) michael.neunteufel@tuwien.ac.at, Lewintan, Peter3 (AUTHOR) peter.lewintan@uni-due.de, Zilian, Andreas1 (AUTHOR) andreas.zilian@uni.lu, Neff, Patrizio3 (AUTHOR) patrizio.neff@uni-due.de
Source: Computer Methods in Applied Mechanics & Engineering. Jan2024:Part A, Vol. 418, pN.PAG-N.PAG. 1p.
Subjects: Sequence spaces, Hilbert space, Metamaterials, Linear dependence (Mathematics)
Abstract: In this work we construct novel H (sym Curl) -conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the div Div -sequence with respect to the H (sym Curl) -space. The elements respect H (Curl) -regularity and their lowest order versions converge optimally for [ H (sym Curl) ∖ H (Curl) ] -fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model. • Introduction of the relaxed micromorphic model with the microdistortion in H (symCurl). • Derivation of the relaxed micromorphic Hilbert space sequence via the divDiv-sequence. • Novel H(symCurl)-conforming elements with optimal convergence in the lowest order. • Benchmarks of the convergence rates of the novel elements for various regularities. • Application of the elements to metamaterial design via the relaxed micromorphic model. [ABSTRACT FROM AUTHOR]
Copyright of Computer Methods in Applied Mechanics & Engineering 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
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DbLabel: Engineering Source
An: 173631428
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  Data: Novel [formula omitted]-conforming finite elements for the relaxed micromorphic sequence.
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  Data: <searchLink fieldCode="AR" term="%22Sky%2C+Adam%22">Sky, Adam</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> adam.sky@uni.lu</i><br /><searchLink fieldCode="AR" term="%22Neunteufel%2C+Michael%22">Neunteufel, Michael</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> michael.neunteufel@tuwien.ac.at</i><br /><searchLink fieldCode="AR" term="%22Lewintan%2C+Peter%22">Lewintan, Peter</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> peter.lewintan@uni-due.de</i><br /><searchLink fieldCode="AR" term="%22Zilian%2C+Andreas%22">Zilian, Andreas</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> andreas.zilian@uni.lu</i><br /><searchLink fieldCode="AR" term="%22Neff%2C+Patrizio%22">Neff, Patrizio</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> patrizio.neff@uni-due.de</i>
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  Data: <searchLink fieldCode="JN" term="%22Computer+Methods+in+Applied+Mechanics+%26+Engineering%22">Computer Methods in Applied Mechanics & Engineering</searchLink>. Jan2024:Part A, Vol. 418, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Sequence+spaces%22">Sequence spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Metamaterials%22">Metamaterials</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+dependence+%28Mathematics%29%22">Linear dependence (Mathematics)</searchLink>
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  Data: In this work we construct novel H (sym Curl) -conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the div Div -sequence with respect to the H (sym Curl) -space. The elements respect H (Curl) -regularity and their lowest order versions converge optimally for [ H (sym Curl) ∖ H (Curl) ] -fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model. • Introduction of the relaxed micromorphic model with the microdistortion in H (symCurl). • Derivation of the relaxed micromorphic Hilbert space sequence via the divDiv-sequence. • Novel H(symCurl)-conforming elements with optimal convergence in the lowest order. • Benchmarks of the convergence rates of the novel elements for various regularities. • Application of the elements to metamaterial design via the relaxed micromorphic model. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Computer Methods in Applied Mechanics & Engineering 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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        Value: 10.1016/j.cma.2023.116494
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Hilbert space
        Type: general
      – SubjectFull: Metamaterials
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      – SubjectFull: Linear dependence (Mathematics)
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      – TitleFull: Novel [formula omitted]-conforming finite elements for the relaxed micromorphic sequence.
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              M: 01
              Text: Jan2024:Part A
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              Y: 2024
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