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.
Magnetostatic problems in fractal domains / Creo, Simone; Lancia, Maria Rosaria; Vernole, Paola; Hinz, Michael; Teplyaev, Alexander. - (2020), pp. 477-502. [10.1142/9789811215537_0015].
Magnetostatic problems in fractal domains
Simone Creo;Maria Rosaria Lancia
;Paola Vernole;
2020
Abstract
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.| File | Dimensione | Formato | |
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