Quantitative homogenization for the case of an interface between two\n heterogeneous media

2019/12/02 by Marc Josien, Josien, Marc, Claudia Raithel +1 · 1 citation
Computer Science · Engineering · #35B27 #35B40 #35J15 #35J25 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1912.00724

openalex publication_date 2019/12/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/08/01

Abstract

In this article we are interested in quantitative homogenization results for\nlinear elliptic equations in the non-stationary situation of a straight\ninterface between two heterogenous media. This extends the previous work\n[Josien, 2019] to a substantially more general setting, in which the\nsurrounding heterogeneous media may be periodic or random stationary and\nergodic. Our main result is a quantification of the sublinearity of a\nhomogenization corrector adapted to the interface, which we construct using an\nimproved version of the method developed in [Fischer and Raithel, 2017]. This\nquantification is optimal up to a logarithmic loss and allows to derive\nalmost-optimal convergence rates.\n

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