Journal Articles and Preprints

1. Clément Cancès, Léonard Monsaingeon, and Andrea Natale. Discretizing the Fokker-Planck equation with second-order accuracy: a dissipation driven approach. arXiv preprint arXiv:2410.03367, 2024.
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2. Thomas O Gallouët, Andrea Natale, and Gabriele Todeschi. Metric extrapolation in the Wasserstein space. arXiv preprint arXiv:2407.10516, 2024.
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3. Thomas Gallouët, Andrea Natale, and Gabriele Todeschi. From geodesic extrapolation to a variational BDF2 scheme for Wasserstein gradient flows. Mathematics of Computation, 2024.
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4. Enrico Facca, Gabriele Todeschi, Andrea Natale, and Michele Benzi. Efficient preconditioners for solving dynamical optimal transport via interior point methods. SIAM Journal on Scientific Computing, 46(3) :A1397–A1422, 2024.
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5. Andrea Natale. Gradient flows of interacting Laguerre cells as discrete porous media flows. arXiv preprint arXiv:2304.05069, 2023.
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6. Andrea Natale and Gabriele Todeschi. A mixed finite element discretization of dynamical optimal transport. Journal of Scientific Computing, 91(2) :1–26, 2022.
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7. Thomas O Gallouët, Quentin Merigot, and Andrea Natale. Convergence of a Lagrangian discretization for barotropic fluids and porous media flow. SIAM Journal on Mathematical Analysis, 54(3) :2990–3018, 2022.
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8. Andrea Natale and Gabriele Todeschi. Computation of optimal transport with finite volumes. ESAIM: M2AN, 55(5) :1847–1871, 2021.
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9. Andrea Natale and Gabriele Todeschi. TPFA Finite Volume approximation of Wasserstein gradient flows. Accepted in the conference: Finite Volumes for Complex Applications, arXiv preprint arXiv:2001.07005, 2020.
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10. Thomas Gallouët, Andrea Natale, and François-Xavier Vialard. Generalized compressible flows and solutions of the H(div) geodesic problem. Archive for Rational Mechanics and Analysis (to appear), arXiv preprint arXiv:1806.10825, 2019.
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11. Andrea Natale and François-Xavier Vialard. Embedding Camassa-Holm equations in incompressible Euler. Journal of Geometric Mechanics, 11(2) :205–223, 2019.
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12. Simone Di Marino, Andrea Natale, Rabah Tahraoui, and François-Xavier Vialard. Metric completion of Diff ([0, 1]) with the H^1 right-invariant metric. arXiv preprint arXiv:1906.09139, 2019.
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13. Andrea Natale and Colin J Cotter. A variational H (div) finite-element discretization approach for perfect incompressible fluids. IMA J. Numer. Anal, 2017.
14. Andrea Natale and Colin J Cotter. Scale-selective dissipation in energy-conserving finite-element schemes for two-dimensional turbulence. Quarterly Journal of the Royal Meteorological Society, 143(705) :1734–1745, 2017.
15. Andrea Natale, Jemma Shipton, and Colin J Cotter. Compatible finite element spaces for geophysical fluid dynamics. Dynamics and Statistics of the Climate System, 1(1) 2016.
16. CJ Cotter, DA Ham, ATT McRae, L Mitchell, and A Natale. On the shallow atmosphere approximation in finite element dynamical cores. arXiv preprint arXiv:1410.3069, 2014.
17. Stefano Discetti, Andrea Natale, and Tommaso Astarita. Spatial filtering improved tomographic PIV. Experiments in fluids, 54(4) :1505, 2013.

Thesis

The full manuscript of my PhD thesis can be found here.