Higher-Order Homogenization for Resolvent Equations of Linearized Elasticity Using the Operator-Asymptotic Approach

The operator-asymptotic approach was introduced by Lim– ubrinić in Lim and ubrinić (2025, Asymptotic Analysis , 141 (4), 211–256) for the homogenization of an ε 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 ε n + 1 in L 2 and ε n in H 1 , for any n .