Orateur
Hélène HIVERT
(Inria - Géosciences Rennes)
Description
In this talk, I will consider the kinetic equation studied in [Bouin, Calvez, Grenier, Nadin, 2023]. I will present the design and analysis of a numerical scheme adapted to the asymptotic behavior of the equation when considered in a large deviations regime. In this regime, the equation degenerates into a nonlocal Hamilton–Jacobi equation, which falls outside the standard frameworks of numerical analysis for Hamilton–Jacobi equations. I will show how a semi-Lagrangian scheme for the original kinetic equation allows one to derive a numerical method suited to the asymptotic regime, and how the convergence of this scheme can be established by relying on the analysis of the well-posedness of the continuous problem.