Publications

In preparation

• E. Bachini, M. Camporese, A. Larese. Shallow water equations versus zero-inertia approximation within a geometrically intrinsic framework. In preparation.
• E. Bachini, C. Janna, A. Larese, G. Scovazzi. Including low-dimensional features in 2D surface models. In preparation.
• E. Bachini and A. Voigt. Intrinsic surface finite element method for vector Laplacian on surfaces. In preparation.
• E. Bachini, M.W. Farthing, M. Putti. Intrinsic surface finite element method on a time-dependent surface. In preparation.
• E. Bachini, C. Dawson, M.W. Farthing, M. Putti. Intrinsic Discontinuos Galerkin scheme for SWE on surfaces. In preparation.

Submitted for peer-review

• E. Bachini and M. Putti. Convergence analysis of the intrinsic surface finite element method. arXiv, 2024. [arXiv:2203.07330]
• E. Abreu, E. Bachini, J. Perez, and M. Putti. A Lagrangian-Eulerian Finite Volume Scheme for ISWE with Localized Discontinuous Topography. SSRN, 2025 [DOI]

Published

• E. Bachini, P. Bandner, T. Jankuhn, M. Nestler, S. Praetorius, A. Reusken, and A. Voigt. Diffusion of tangential tensor fields: numerical issues and influence of geometric properties. J. Numer. Math., 32(1):55-75, 2024. [DOI] [code]
• E. Bachini, V. Krause, I. Nitschke, A. Voigt. Derivation and simulation of a two-phase fluid deformable surface model. J. Fluid Mech., 977:A41, 2023. [DOI]
• E. Bachini, V. Krause, A. Voigt. The interplay of geometry and coarsening in multicomponent lipid vesicles under the influence of hydrodynamics. Phys. Fluids, 35:042102, 2023. [DOI]
• E. Abreu, E. Bachini, J. Perez, and M. Putti. A geometrically intrinsic Lagrangian-Eulerian scheme for 2D shallow water equations with variable topography and discontinuous data. Appl. Math. Comput., 443:127776, 2023. [DOI]
• E. Bachini, E. Bellizia, M. Putti, A. D’Alpaos, and M. Ghinassi. Two-dimensional model of flow and transport in porous media: linking heterogeneous anisotropy with stratal patterns in meandering tidal channel deposits of the Venice lagoon (Italy). Environ. Modell. Softw., 157:105535, 2022. [DOI]
• E. Bachini, G. Manzini, and M. Putti. Arbitrary-order intrinsic virtual element method for elliptic equations on surfaces. Calcolo, 58(30), 2021. [DOI]
• E. Bachini, M. W. Farthing, and M. Putti. Intrinsic finite element method for advection-diffusion-reaction equations on surfaces. J. Comp. Phys., 424, 2021. [DOI]
• E. Bachini and M. Putti. Geometrically intrinsic modeling of shallow water flows. ESAIM Math. Model. Num. Anal., 54(6):2125–2157, 2020. [DOI]
• D. Gomes et al. Existence of positive solutions for an approximation of stationary mean-field games. Involve, a Journal of Mathematics, 10(3):473–493, 2017. [DOI]

Doctoral thesis

• E. Bachini. Numerical methods for Shallow Water Equations on regular surfaces. PhD thesis, University of Padua, 2020. [url]