  We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch
type. We prove existence and uniqueness results for both the fractal and
pre-fractal problems and we investigate the convergence of the pre-fractal
solutions to the limit fractal one. We consider the numerical approximation of
the pre-fractal problems via FEM and we prove a priori error estimates. Some
numerical simulations are also shown. Our long term motivation includes
studying problems that appear in quantum physics in fractal domains.
