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arXiv · 1805.08262

Magnetostatic problems in fractal domains

Simone Creo·Maria Rosaria Lancia·Paola Vernole·Michael Hinz·Alexander Teplyaev
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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.

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BibTeXRIS

Simone Creo, Maria Rosaria Lancia, Paola Vernole, Michael Hinz, Alexander Teplyaev. 2018-05-21. Magnetostatic problems in fractal domains. https://arxiv.org/abs/1805.08262

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