Samuele Ferri

Samuele Ferri, Chiara Giraudo, Valerio Loi et al.

In the present paper, we analyze in detail the spectral features of the matrix sequences arising from the Taylor-Hood $\mathbb{P}_2$-$\mathbb{P}_1$ approximation of variable viscosity for $2d$ Stokes problem under weak assumptions on the regularity of the diffusion. Localization and distributional spectral results are provided, accompanied by numerical tests and visualizations. A preliminary study of the impact of our findings on the preconditioning problem is also presented. A final section with concluding remarks and open problems ends the current work.

Elishan Christian Braun, Gabriella Bretti, Samuele Ferri et al.

In this paper we introduce a new mathematical model describing the erosion process caused in carbonate stones by the dissolution of the porous matrix due to the penetration of carbonic acid present in the environment. Such model is formulated as nonlinear reaction-transport system in porous media governed by Darcy flow. We propose a numerical algorithm based on finite difference approximation that relies on level-set method at the boundaries and we show numerical tests that are in accordance with the literature in terms of the advancement of the erosion front.