Ricerc@Sapienza

We study a Stokes flow in a cylindrical-type fractal domain with homogeneousDirichlet boundary conditions. We consider its numerical approximation bymixed methods: finite elements in space and finite differences in time. We intro-duce a suitably refined mesh `a la Grisvard, which in turn will allow us to obtainan optimal a priori error estimate

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.

We study a nonlocal Venttsel' problem in a nonconvex bounded domain with
a Koch-type boundary. Regularity results of the strict solution are proved in
weighted Sobolev spaces. The numerical approximation of the problem is carried
out, and optimal a priori error estimates are obtained.