Fibre homogenisation for time-dependent problems

TL;DR

This paper introduces a method for deriving operator error estimates between solutions of rapidly oscillating time-dependent equations and their homogenised versions, with applications to wave, heat, and thermoelastic systems.

Contribution

It presents a novel approach for operator error estimates in homogenisation of time-dependent problems, extending previous methods to evolutionary equations.

Findings

Effective error estimates for wave, heat, and thermoelastic systems

Applicable to a broad class of evolutionary equations

Enhances understanding of homogenisation in dynamic problems

Abstract

In this article we provide a method for establishing operator-type error estimates between solutions to rapidly oscillating evolutionary equations and their homogenised counter parts. This method is exemplified by applications to the wave, heat and finally thermoelastic evolutionary systems.