7 citations · 10 across the 8 of their papers we have counts for
10 papers
Numerical analysis of the large deviation regime of a kinetic equation with a nonlocal Hamilton-Jacobi limit
Hélène Hivert, Tino Laidin
We develop and study an asymptotic-preserving (AP) numerical scheme for a linear kinetic equation in a large deviation regime. After applying a Hopf-Cole transform to the distribut…
Structure-preserving scheme for fractional nonlinear diffusion equations
Hélène Hivert, Florian Salin
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations genera…
Numerical approximation of a class of constrained Hamilton-Jacobi equations
Benoît Gaudeul, Hélène Hivert
In this paper, we introduce a framework for the discretization of a class of constrained Hamilton-Jacobi equations, a system coupling a Hamilton-Jacobi equation with a Lagrange mul…
Concentration in Lotka-Volterra parabolic equations: an asymptotic-preserving scheme
Vincent Calvez, Hélène Hivert, Havva Yoldaş
In this paper, we introduce and analyze an asymptotic-preserving scheme for Lotka-Volterra parabolic equations. It is a class of nonlinear and nonlocal stiff equations, which descr…
On a structure-preserving numerical method for fractional Fokker-Planck equations
Nathalie Ayi, Maxime Herda, Hélène Hivert +1
In this paper, we introduce and analyse numerical schemes for the homogeneous and the kinetic Lévy-Fokker-Planck equation. The discretizations are designed to preserve the main fea…
A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium
Nathalie Ayi, Maxime Herda, Hélène Hivert +1
In this paper we are interested in the large time behavior of linear kinetic equations with heavy-tailed local equilibria. Our main contribution concerns the kinetic Lévy-Fokker-Pl…
Horizontal gene transfer: numerical comparison between stochastic and deterministic approaches
Vincent Calvez, Susely Figueroa Iglesias, Hélène Hivert +3
Horizontal gene Transfer (HT) denotes the transmission of genetic material between two living organisms, while the vertical transmission refers to a DNA transfer from parents to th…
An asymptotic preserving scheme for front propagation in a kinetic reaction-transport equation
Hélène Hivert
In this work, we propose an asymptotic preserving scheme for a non-linear kinetic reaction-transport equation, in the regime of sharp interface. With a non-linear reaction term of…
Multiscale numerical schemes for kinetic equations in the anomalous diffusion limit
Nicolas Crouseilles, Hélène Hivert, Mohammed Lemou
We construct numerical schemes to solve kinetic equations with anomalous diffusion scaling. When the equilibrium is heavy-tailed or when the collision frequency degenerates for sma…
Numerical schemes for kinetic equations in the diffusion and anomalous diffusion limits. Part I: the case of heavy-tailed equilibrium
Nicolas Crouseilles, Hélène Hivert, Mohammed Lemou
In this work, we propose some numerical schemes for linear kinetic equations in the diffusion and anomalous diffusion limit. When the equilibrium distribution function is a Maxwell…