Magnetostatic problems in fractal domains
Mathematical Physics
2018-12-04 v2 Analysis of PDEs
Functional Analysis
Metric Geometry
math.MP
Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.1805.08262,
title = {Magnetostatic problems in fractal domains},
author = {Simone Creo and Maria Rosaria Lancia and Paola Vernole and Michael Hinz and Alexander Teplyaev},
journal= {arXiv preprint arXiv:1805.08262},
year = {2018}
}