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.
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications Analysis, Probability and Mathematical Physics on Fractals
fractal surfaces; trace theorems; asymptotic analysis; weighted sobolev spaces; finite element method
02 Pubblicazione su volume::02a Capitolo o Articolo
Magnetostatic problems in fractal domains / Creo, Simone; Lancia, Maria Rosaria; Vernole, Paola; Hinz, Michael; Teplyaev, Alexander. - (2020), pp. 477-502. [10.1142/9789811215537_0015].
File allegati a questo prodotto
File Dimensione Formato  
Creo_Magnetostatic_2020.pdf

solo gestori archivio

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 700.52 kB
Formato Adobe PDF
700.52 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1470536
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? ND
social impact