Introduction to PDE based multiscale problems and to approaches for their treatment. Special attention will be given to the following topics:
- homogenisation of elliptic equations with oscillating coefficients,
- classification of multiscale problems,
- advanced numerical algorithms for PDEs and systems of PDEs with oscillating coefficients (including multiscale finite element method, multiscale finite volume method, heterogeneous multiscale method, subgrid approach),
- numerical approaches for stochastic elliptic PDE.