Work

Optimal Convergence Rates in Multiscale Elliptic Homogenization

Year: 2026

Type: article

Abstract: ABSTRACT This paper is devoted to the quantitative homogenization of multiscale elliptic operator , where , , and . We assume that is 1‐periodic in each and real analytic. Classically, the method of reiterated homogenization has been applied to study this multiscale elliptic operator, which leads to a convergence rate limited by the ratios . In the present paper, under the assumption of real analytic coefficients, we introduce the so‐called multiscale correctors and more accurate effective operators, and improve the ratio part of the convergence rate to . This convergence rate is optimal in the sense that cannot be replaced by a larger constant. As a byproduct, the uniform Lipschitz estimate is established under a mild double‐log scale‐separation condition.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.70047

Authors: Weisheng Niu, Yao Xu, Jinping Zhuge

Institutions: Anhui University, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G2503836298, G7153082605, G7224195231, G7344475885, G8533620077