For partial differential equation with multiple geometric scales we analyse the asymptotic behaviour of solutions. This can be done for example with the method of matched asymptotic expansions or homogenisation techniques. Applications are thin conducting sheets in electromagnetic field simulation, viscoacoustic boundary layers, multiperforated acoustic liners for noise absorption or propagation of waves outside of the computational domains. For the asymptotic expansions both smooth domains and Lipschitz domains, for which corner singularities interact with boundary layer behaviour, are of interest.
We aim to understand the behaviour on smaller and larger scales and to obtain macroscopic models with effective boundary conditions. Moreover, for macroscopic models with such boundary conditions we analyse variational formulations and discretisations by finite element methods.
