Efficiency of approximate boundary conditions for corner domains coated with thin layers
Grégory Vial · Comptes Rendus Mathématique · 2005
In this Note, we consider an interface problem posed in a bounded domain with thin layer. In the case of a smooth domain, approximate boundary conditions (also called impedance conditions) are known to approximate in a precise way the effect of the layer, as its thickness goes to zero. We investigate here the efficiency of such conditions when the domain has a corner; we show that it deteriorates when the opening of the corner angle grows, giving optimal estimates thanks to multiscale asymptotic expansions. Numerical results are given, which illustrate these estimates.