40 citations · 92 across the 20 of their papers we have counts for
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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)…
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…
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…
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…
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…
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 discrete functional inequalities for some finite volume schemes
Marianne Bessemoulin-Chatard, Claire Chainais-Hillairet, Francis Filbet
We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincaré-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint…