Multiscale finite element methods for heat equation in three dimension honeycomb structure

Abstract

Honeycomb structure is a kind of useful typical cellular solid. It has good physics, mechanism and heat properties because of its characteristics of cavity. The difficult to study the heat problem in honeycomb structure is the complexity of the geometric configuration. It is difficult to solve the problem by using directly finite element method because the subdivision is very difficult to obtain and very large scale computing and memory capacity. In this paper, we shall overcome above difficulties and study the heat equation in three dimensional honeycomb structure. A multiscale finite element method with high accuracy is presented. We derive the rigorous proofs of all convergence results. © 2011 Springer-Verlag.