Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911124611399680 |
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| author | Lim, Yi-Sheng Žubrinić, Josip |
| author_facet | Lim, Yi-Sheng Žubrinić, Josip |
| contents | The operator-asymptotic approach was introduced by Lim-Žubrinić in [Asymptotic Analysis. 141(4), p. 211-256 (2025)] for the homogenization of an $\varepsilon\mathbb{Z}^d$-periodic composite media. In this article, we consider the setting of three-dimensional linearized elasticity, and extend the approach to obtain higher-order convergence rates. In particular, we consider the so-called ``Bloch approximation'' for vector-valued functions with compact Fourier support, and demonstrate that under such data, the approach provides an expansion that yields an error of order $\varepsilon^{n+1}$ in $L^2$ and $\varepsilon^n$ in $H^1$, for any $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach Lim, Yi-Sheng Žubrinić, Josip Analysis of PDEs The operator-asymptotic approach was introduced by Lim-Žubrinić in [Asymptotic Analysis. 141(4), p. 211-256 (2025)] for the homogenization of an $\varepsilon\mathbb{Z}^d$-periodic composite media. In this article, we consider the setting of three-dimensional linearized elasticity, and extend the approach to obtain higher-order convergence rates. In particular, we consider the so-called ``Bloch approximation'' for vector-valued functions with compact Fourier support, and demonstrate that under such data, the approach provides an expansion that yields an error of order $\varepsilon^{n+1}$ in $L^2$ and $\varepsilon^n$ in $H^1$, for any $n$. |
| title | Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.19388 |