Nonlinear transmission conditions for thin highly conductive interphases of curvilinear shape

We consider heat transfer problem in a composite ceramic featuring a thin nonlinear interphase layer with distinctively different characteristics (high thermal conductivity, apart from the mentioned physical size). The presence of an interphase may be problematic for the classical FEM approach in terms of technical implementation, accuracy and stability of the results. We avoid the potential issues by replacing the interphase in the model with a zero thickness imperfect nonlinear interface with two transmission conditions. These conditions are carefully derived using asymptotic analysis and aim at preserving the physical properties of the original interphase layer now absent in the model, thus ensuring an accurate solution. Numerical examples with particular attention to various physical and geometrical aspects illustrate the validity of the described approach.