40 citations · 92 across the 20 of their papers we have counts for
25 papers
A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
Matthieu Alfaro, Claire Chainais-Hillairet, Flore Nabet
In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (…
Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers
Dilara Abdel, Alain Blaustein, Claire Chainais-Hillairet +2
We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other application…
Finite Volumes for a dissipative free boundary problem
Clément Cancès, Claire Chainais-Hillairet, Amélie Dupouy
We study a toy model for the evolution of the oxygen concentration in an oxide layer. It consists in a transient convection diffusion equation in a one-dimensional domain of variab…
Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models
Dilara Abdel, Maxime Herda, Martin Ziegler +3
In this paper, we present the numerical analysis and simulations of a multi-dimensional memristive device model. Memristive devices and memtransistors based on two-dimensional (2D)…
Cross-diffusion systems coupled via a moving interface
Clément Cancès, Jean Cauvin-Vila, Claire Chainais-Hillairet +1
We propose and study a one-dimensional model which consists of two cross-diffusion systems coupled via a moving interface. The motivation stems from the modelling of complex diffus…
Long time behavior of the field-road diffusion model: an entropy method and a finite volume scheme
Matthieu Alfaro, Claire Chainais-Hillairet
We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in…
Structure Preserving Finite Volume Approximation of Cross-Diffusion Systems Coupled by a Free Interface
Clément Cancès, Jean Cauvin-Vila, Claire Chainais-Hillairet +1
We propose a two-point flux approximation finite-volume scheme for the approximation of two cross-diffusion systems coupled by a free interface to account for vapor deposition. The…
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells
Dilara Abdel, Claire Chainais-Hillairet, Patricio Farrell +1
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 nonlinea…
Mathematical analysis of a thermodynamically consistent reduced model for iron corrosion
Clément Cancès, Claire Chainais-Hillairet, Benoît Merlet +2
We are interested in a reduced model for corrosion of iron, in which ferric cations and electrons evolve in a fixed oxide layer subject to a self-consistent electrostatic potential…
Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches
Claire Chainais-Hillairet, Maxime Herda, Simon Lemaire +1
We are interested in the long-time behaviour of approximate solutions to heterogeneous and anisotropic linear advection-diffusion equations in the framework of hybrid finite volume…
bounds for numerical solutions of noncoercive convection-diffusion equations
Claire Chainais-Hillairet, Maxime Herda
In this work, we apply an iterative energy method à la de Giorgi in order to establish bounds for numerical solutions of noncoercive convection-diffusion equations wit…
Large time behavior of nonlinear finite volume schemes for convection-diffusion equations
Clément Cancès, Claire Chainais-Hillairet, Maxime Herda +1
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…
A numerical analysis focused comparison of several Finite Volume schemes for an Unipolar Degenerated Drift-Diffusion Model
Clément Cancès, Claire Chainais-Hillairet, Jürgen Fuhrmann +1
In this paper, we consider an unipolar degenerated drift-diffusion system where the relation between the concentration of the charged species and the chemical potential is…
Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations
Claire Chainais-Hillairet, Maxime Herda
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and N…
Large time behavior of a two phase extension of the porous medium equation
Ahmed Ait Hammou Oulhaj, Clément Cancès, Claire Chainais-Hillairet +1
We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to iden…
Convergence of a Finite-Volume Scheme for a Degenerate Cross-Diffusion Model for Ion Transport
Clément Cancès, Claire Chainais-Hillairet, Anita Gerstenmayer +1
An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations…
Numerical analysis of a nonlinear free-energy diminishing Discrete Duality Finite Volume scheme for convection diffusion equations
Clément Cancès, Claire Chainais-Hillairet, Stella Krell
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even o…
Uniform L estimates for approximate solutions of the bipolar drift-diffusion system
Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Ansgar Jüngel
We establish uniform L bounds for approximate solutions of the drift-diffusion system for electrons and holes in semiconductor devices, computed with the Schar-fetter-Gumm…
Exponential decay of a finite volume scheme to the thermal equilibrium for drift--diffusion systems
Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet
In this paper, we study the large--time behavior of a numerical scheme discretizing drift-- diffusion systems for semiconductors. The numerical method is finite volume in space, im…
Convergence of a Finite Volume Scheme for a Corrosion Model
Claire Chainais-Hillairet, Pierre-Louis Colin, Ingrid Lacroix-Violet
In this paper, we study the numerical approximation of a system of partial dif-ferential equations describing the corrosion of an iron based alloy in a nuclear waste repository. In…
A Finite-Volume Scheme for a Spinorial Matrix Drift-Diffusion Model for Semiconductors
Claire Chainais-Hillairet, Ansgar Jüngel, Polina Shpartko
An implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for t…
Entropy-dissipative discretization of nonlinear diffusion equations and discrete Beckner inequalities
Claire Chainais-Hillairet, Ansgar Jüngel, Stefan Schuchnigg
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy se…
Study of a fully implicit scheme for the drift-diffusion system. Asymptotic behavior in the quasi-neutral limit
Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Marie-Hélène Vignal
In this paper, we are interested in the numerical approximation of the classical time-dependent drift-diffusion system near quasi-neutrality. We consider a fully implicit in time a…
On the existence of solutions for a drift-diffusion system arising in corrosion modelling
Ingrid Lacroix-Violet, Claire Chainais-Hillairet
In this paper, we consider a drift-diffusion system describing the corrosion of an iron based alloy in a nuclear waste repository. In comparison with the classical drift-diffusion…