@Article{CiCP-14-4,
author = {},
title = {Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain},
journal = {Communications in Computational Physics},
year = {2013},
volume = {14},
number = {4},
pages = {1027--1057},
abstract = {<p style="text-align: justify;">In this paper a second-order two-scale (SOTS) analysis method is developed
for a static heat conductive problem in a periodical porous domain with radiation
boundary condition on the surfaces of cavities. By using asymptotic expansion for
the temperature field and a proper regularity assumption on the macroscopic scale,
the cell problem, effective material coefficients, homogenization problem, first-order
correctors and second-order correctors are obtained successively. The characteristics
of the asymptotic model is the coupling of the cell problems with the homogenization temperature field due to the nonlinearity and nonlocality of the radiation boundary condition. The error estimation is also obtained for the original solution and the
SOTS&#39;s approximation solution. Finally the corresponding finite element algorithms
are developed and a simple numerical example is presented.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.290612.180113a},
url = {https://global-sci.com/article/80588/second-order-two-scale-analysis-method-for-the-heat-conductive-problem-with-radiation-boundary-condition-in-periodical-porous-domain}
}