# Error estimate for a homogenization problem involving the Laplace-Beltrami operator

## TL;DR

This paper provides an error estimate and concentration result for heat conduction models in composite materials with microscopic periodic structures and thermally active membranes, advancing understanding of homogenization in such systems.

## Contribution

It introduces a novel error estimate for a homogenization problem involving the Laplace-Beltrami operator in composite materials with membranes.

## Key findings

- Established a concentration result for the model
- Derived an explicit error estimate for the homogenization approximation
- Enhanced understanding of heat conduction in complex composite structures

## Abstract

In this paper we prove a concentration result and an error estimate for a model of heat conduction in composite materials having a microscopic structure arranged in a perodic array and thermally active membranes separating the heat conductive phases.