Second-Order Two-Scale Analysis Method for the Heat Conductive Problem with Radiation Boundary Condition in Periodical Porous Domain (Communications in Computational Physics, 2013)
In this paper a second-order two-scale (SOTS) analysis method is developedfor a static heat conductive problem in a periodical porous domain with radiationboundary condition on the surfaces of cavities. By using asymptotic expansion forthe temperature field and a proper regularity assumption on the macroscopic scale,the cell problem, effective material coefficients, homogenization problem, first-ordercorrectors and second-order correctors are obtained successively. The characteristicsof 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 theSOTS's approximation solution. Finally the corresponding finite element algorithmsare developed and a simple numerical example is presented.