Until December 2021, I was a PhD student at Université Paris-Saclay, under the supervision of Jean-Marie Mirebeau and Frédéric Bonnans. During my PhD, I designed and studied monotone finite difference schemes for some degenerate elliptic partial differential equations, such as the Hamilton-Jacobi-Bellman and Monge-Ampère equations, on Cartesian grids, using tools originating from the theory of the geometry of low-dimensional lattices.
- G. Bonnet and J.‑M. Mirebeau. Monotone discretization of the Monge-Ampère equation of optimal transport. ESAIM: Mathematical Modelling and Numerical Analysis, 56(3):815–865, 2022 (link, HAL preprint).
- J. F. Bonnans, G. Bonnet, and J.‑M. Mirebeau. A linear finite-difference scheme for approximating Randers distances on Cartesian grids. ESAIM: Control, Optimisation and Calculus of Variations, 28:45:1–45:49, 2022 (link, HAL preprint).
- J. F. Bonnans, G. Bonnet, and J.‑M. Mirebeau. Second order monotone finite differences discretization of linear anisotropic differential operators. Mathematics of Computation, 90(332):2671–2703, 2021 (link, HAL preprint).
- J. F. Bonnans, G. Bonnet, and J.‑M. Mirebeau. Monotone and second order consistent scheme for the two dimensional Pucci equation. In F. J. Vermolen and C. Vuik, editors, Numerical Mathematics and Advanced Applications ENUMATH 2019, pages 733–742. Springer, 2021 (link, HAL preprint).
- Monotone discretization of anisotropic four-dimensional differential operators using Voronoi’s first reduction.
- Virtual element methods, adaptivity.
- Finite difference discretization of degenerate elliptic equations using Voronoi’s first reduction, Workshop on the theory and numerics of Mean Field Games and Hamilton-Jacobi equations, June 2022, Rome, Italy.
- Monotone finite difference discretization of the Monge-Ampère equation of optimal transport, Oberwolfach Workshop on Numerical Methods for Fully Nonlinear and Related PDEs, June 2021, Oberwolfach, Germany.
- A linear finite difference scheme to approach Randers distances on Cartesian grids, SMAI 2021, June 2021, La Grande-Motte, France. Parallel session: Numerical methods.
- Efficient discretizations of non-linear and anisotropic PDEs on Cartesian grids, ICIAM 2019, July 2019, Valencia, Spain. Mini-symposium: Anisotropic variational models and anisotropic PDEs.
- Efficient discretizations of non-linear and anisotropic PDEs on Cartesian grids, Mafelap 2019, June 2019, Brunel University London, UK. Mini-symposium: Numerical methods for nonvariational PDEs.
At Université Paris-Saclay, I teached:
I was a coorganizer of the CJC-MA 2021 conference for young researchers in France.