Abstract
This paper deals with multiscale analysis, by using the correctors, of a nonlinear heat transmission problem in a periodic microscopic structure with multiple components. The occurring nonlinearity is related to the flux condition at the interface between the two parts of the medium. In this work, we present first the multiscale asymptotic expansion of the solution for this kind of problems and the strong convergence of the asymptotic expansion to the solution of the multiscale model. Then, we introduce a numerical algorithm based on the multiscale method for solving this problem. Finally, in order to confirm the efficiency of the proposed algorithm, some numerical results obtained through finite element approximations are presented.
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