Homogenization: multiscale modeling, analysis and simulation

The 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 homogenised elliptic, parabolic, and hyperbolic equations, (iii) implementation and numerical simulation of homogenised 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 homogenisation of second-order linear elliptic equations, (viii) passage to the homogenisation limit and derivation of corrector estimates.