The presence of atomic oxygen at internal metal-ceramic oxide interfaces significantly affects the physical properties of the interfaces which in turn affects the bulk properties of the material. This problem is addressed for the model composite system Ag-MgO from a phenomenological point of view using a lattice-based Monte Carlo method and a finite element method extended with special user-subroutines. We simulate the time dependence of oxygen depth and contour profiles. We are able to show very good agreement between these two methods.