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arXiv · 2508.19388

Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach

Yi-Sheng Lim·Josip Žubrinić
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Abstract

The operator-asymptotic approach was introduced by Lim-\v{Z}ubrini\'c 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 $n$.

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Yi-Sheng Lim, Josip Žubrinić. 2025-08-26. Higher-order homogenization for equations of linearized elasticity using the operator-asymptotic approach. https://arxiv.org/abs/2508.19388

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