Two-Scale Convergence Homogenization Techniques and Multiscale Modeling

1.recognise relevant separated scales and types of multiscale problems; 2. select appropriate small parameters required for asymptotic developments; 3. formally scale up microscopic systems using arguments from asymptotic two-scale homogenisation; 4.rigorously scale up microscopic systems with compactness and arguments from two-scale convergence; 5. determine the quality of certain homogenisation strategies by using information from corrector estimates; 6. numerically illustrate the significance of homogenisation of partial differential equations formulated in perforated domains