Magnetostatic Problems in Fractal Domains
Simone Creo, Maria Rosaria Lancia, Paola Vernole, Michael Hinz, Alexander Teplyaev · Fractals and dynamics in mathematics, science and the arts · 2020
We consider a magnetostatic problem in a three-dimensional “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 give 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.