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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]
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Database: Engineering Source
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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]
ISSN:00457825
DOI:10.1016/j.cma.2023.116494