  This study develops a novel multiscale computational method for heat
conduction problems of composite structures with diverse periodic
configurations in different subdomains. Firstly, the second-order two-scale
(SOTS) solutions for these multiscale problems are successfully obtained based
on asymptotic homogenization method. Then, the error analysis in the pointwise
sense is given to illustrate the importance of developing SOTS solutions.
Furthermore, the error estimates for the SOTS approximate solutions in the
integral sense is presented. In addition, a SOTS numerical algorithm is
proposed to effectively solve these problems based on finite element method.
Finally, some numerical examples verify the feasibility and effectiveness of
the SOTS numerical algorithm we proposed.
