An Optimal Mesh Generation for Domains with Koch Type Boundaries

We consider the numerical approximation for a 2D second order parabolic transmission problem across a pre-fractal interface K_n of Koch type; the layer K_n, a polygonal curve, divides a given domain into two non-convex sub-domains \Omega^i_n. The approximation is carried out by a FEM discretization for the space variable and a finite difference scheme in time. The two main difficulties in the approximation and simulations of this type of problems are the generation of a suitable mesh to possibly achieve an optimal rate of convergence and to limit the intrinsic computational cost of numeric approximations. In this talk we will focus on the construction of a mesh compliant with the so-called "Grisvard" conditions which will allow us to obtain an optimal rate of convergence both in space and in time.