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Author: Reichelt, Sina × Subject: corrector estimates ×

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    Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains
    (Chichester, West Sussex : Wiley, 2020) Kovtunenko, Victor A.; Reichelt, Sina; Zubkova, Anna V.
    This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector. © 2019 The Authors. Mathematical Methods in the Applied Sciences published by John Wiley & Sons Ltd.
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    Corrector estimates for a thermo-diffusion model with weak thermal coupling
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Muntean, Adrian; Reichelt, Sina
    The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology weak thermal coupling refers here to the variable scaling in terms of the small homogenization parameter " of the heat conduction diffusion interaction terms, while the high-contrast is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with -independent estimates for the thermal and concentration fields and for their coupled fluxes.