I am a postdoctoral researcher in applied mathematics at University of Maryland, in the team of Ricardo Nochetto. Previously, I worked with Andrea Cangiani at SISSA and with Jean-Marie Mirebeau and Frédéric Bonnans at Université Paris-Saclay and École polytechnique. My main research topic so far is finite-difference and finite-element-type numerical schemes for nonlinear degenerate elliptic PDEs such as the Hamilton-Jacobi-Bellman and Monge-Ampère equations, and for linear nondivergence form diffusion problems.

Research

Publications

• J. F. Bonnans, G. Bonnet, and J.‑M. Mirebeau. Monotone discretization of anisotropic differential operators using Voronoi’s first reduction. Submitted 2022 (HAL preprint).
• 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, code).
• 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).

Works under finalization

• With A. Cangiani and R. Nochetto. Virtual element discretization of linear and nonlinear nondivergence form diffusion equations.

Talks

• Discretization of the second boundary value problem for the Monge-Ampère equation using Voronoi’s first reduction, SIAM Conference on Computational Science and Engineering 2023, March 2023, Amsterdam, Netherlands
• 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.

PhD manuscript

• Monotone finite difference discretization of degenerate elliptic partial differential equations using Voronoi’s first reduction.

Teaching

I was involved in teaching the following courses:

• Math 246H — Differential Equations for Engineers Honors, University of Maryland (primary teacher).
• MATLAB refresher course, Master of Applied Mathematics, Université Paris-Saclay (primary teacher).
• Numerical analysis with Python, Bachelor of Mathematics, Université Paris-Saclay.
• Matrix analysis and optimization, Bachelor of Mathematics, Université Paris-Saclay.

Other activities

I was a coorganizer of the CJC-MA 2021 conference for young researchers in France.

Curriculum vitae

• 2023: postdoctoral associate at University of Maryland.
• 2022: postdoctoral researcher at SISSA.
• 2018–2021: PhD at Université Paris-Saclay and École polytechnique.
• 2017–2018: MSc in Mathematics of Modelling at Sorbonne Université.

I was born in June, 1997.