Structure preserving schemes for Fokker–Planck equations of irreversible processes

C Liu, Y Gao, X Zhang - Journal of Scientific Computing, 2024 - Springer
In this paper, we construct structure preserving schemes for solving Fokker–Planck
equations associated with irreversible processes. The proposed method is first order in time …

Long-time behaviour of hybrid finite volume schemes for advection–diffusion equations: linear and nonlinear approaches

C Chainais-Hillairet, M Herda, S Lemaire… - Numerische …, 2022 - Springer
We are interested in the long-time behaviour of approximate solutions to anisotropic and
heterogeneous linear advection–diffusion equations in the framework of hybrid finite volume …

Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations

M Bessemoulin-Chatard, M Herda, T Rey - Mathematics of Computation, 2020 - ams.org
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one-
dimensional linear kinetic equations, with either a Fokker–Planck or linearized BGK collision …

On a discrete framework of hypocoercivity for kinetic equations

A Blaustein, F Filbet - Mathematics of Computation, 2024 - ams.org
We propose and study a fully discrete finite volume scheme for the linear Vlasov-Fokker-
Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This …

Large time behavior of nonlinear finite volume schemes for convection-diffusion equations

C Cancès, C Chainais-Hillairet, M Herda, S Krell - SIAM Journal on Numerical …, 2020 - SIAM
In this contribution we analyze the large time behavior of a family of nonlinear finite volume
schemes for anisotropic convection-diffusion equations set in a bounded bidimensional …

Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems

J Jung, V Perrier - IMA Journal of Numerical Analysis, 2023 - academic.oup.com
This article is dedicated to the long time behavior of a finite volume approximation of general
symmetrizable linear hyperbolic system on a bounded domain. In the continuous case this …

Discrete hypocoercivity for a nonlinear kinetic reaction model

M Bessemoulin-Chatard, T Laidin… - IMA Journal of Numerical …, 2024 - academic.oup.com
In this article we propose a finite-volume discretization of a one-dimensional nonlinear
reaction kinetic model proposed in, which describes a two-species recombination …

Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator

M Heida, M Kantner, A Stephan - ESAIM: Mathematical Modelling …, 2021 - esaim-m2an.org
We introduce a family of various finite volume discretization schemes for the Fokker–Planck
operator, which are characterized by different Stolarsky weight functions on the edges. This …

On the square-root approximation finite volume scheme for nonlinear drift-diffusion equations

C Cancès, J Venel - Comptes Rendus …, 2023 - comptes-rendus.academie-sciences …
We study a finite volume scheme for the approximation of the solution to convection diffusion
equations with nonlinear convection and Robin boundary conditions. The scheme builds on …

Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells

D Abdel, C Chainais-Hillairet, P Farrell… - IMA Journal of …, 2024 - academic.oup.com
In this paper, we consider a drift-diffusion charge transport model for perovskite solar cells,
where electrons and holes may diffuse linearly (Boltzmann approximation) or nonlinearly …