Homogenization: Multiscale Modeling, Analysis and Simulation

Karlstad University

The PhD course covers the following:
(i) scaling and upscaling based on two-scale asymptotics for partial differential equations and systems of equations with oscillating coefficients formulated in perforated domains,
(ii) derivation of explicit formulas for effective coefficients and homogenized elliptic, parabolic, and hyperbolic equations,
(iii) implementation and numerical simulation of homogenized linear elliptic equations,
(iv) derivation of Darcy's law for perforated domains,
(v) introduction to weak convergence for linear elliptic partial differential equations,
(vi) the concepts of two-scale convergence and compactness,
(vii) application of two-scale convergence for homogenization of second-order linear elliptic equations,
(viii) passage to the homogenization limit and derivation of corrector estimates.

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