We consider the numerical approximation for a 2D advection-diffusion problem in a domain whose boundary is a prefractal mixture curve of Koch type. The presence of a prefractal boundary deteriorates the regularity of the solution and hence the rate of convergence of the numerical approximations. The two main difficulties arising in the numerical simulations of this type of problems are the generation of a suitable mesh to possibly achieve an optimal rate of convergence and the limitation of the computational costs.
We obtain a priori error estimates. By exploiting some regularity results for the solution we build a mesh compliant with the so-called "Grisvard" conditions thus allowing to achieve an optimal rate of convergence.