Numerical approximation of transmission problems across Koch-type highly conductive layers

We prove a priori error estimates for a parabolic second order transmission problem across a prefractal interface Kn of Koch type which divides a given domain Ω into two non-convex sub-domains Ωni. By exploiting some regularity results for the solution in Ωni we build a suitable mesh, compliant with the so-called “Grisvard” conditions, which allows to achieve an optimal rate of convergence for the semidiscrete approximation of the prefractal problem by Galerkin method. The discretization in time is carried out by the θ-method.