I am interested in the analysis of partial differential equations and the conception of structure preserving schemes for their numerical resolution.
Keywords: Partial differential equations (PDEs), numerical analysis, kinetic PDEs, parabolic PDEs, asymptotic behaviors, entropy methods, hypocoercivity, hydrodynamic limits, finite volume schemes, positive polynomials, plasma physics, semiconductors, applications in biology.
Numerical analysis and simulation of lateral memristive devices: Schottky, ohmic, and multi-dimensional electrode models - (preprint)
with Dilara Abdel, Martin Ziegler, Claire Chainais-Hillairet, Benjamin Spetzler and Patricio Farrell - submitted, 2024.
A finite volume scheme for the local sensing chemotaxis model - (preprint)
with Ariane Trescases and Antoine Zurek - submitted, 2024.
Convergence and long-time behavior of finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion - (preprint)
with Clément Cancès and Annamaria Massimini - submitted, 2024.
Charge transport systems with Fermi-Dirac statistics for memristors - (preprint)
with Ansgar Jüngel and Stefan Portisch - submitted, 2024.
Well-posedness and long-time behavior for self-consistent Vlasov-Fokker-Planck equations with general potentials - (preprint)
with Pierre Gervais - submitted, 2024.
On a Vlasov-Fokker-Planck equation for stored electron beams - (preprint)
with Ludovic Cesbron - Journal of Differential Equations, 2024.
Wasserstein contraction for the stochastic Morris-Lecar neuron model - (preprint)
with Pierre Monmarché and Benoît Perthame - Kinetic and Related Models, 2024.
Numerical analysis of a finite volume scheme for charge transport in perovskite solar cells - (preprint)
with Dilara Abdel, Claire Chainais-Hillairet and Patricio Farrell - IMA Journal of Numerical Analysis, 2024.
Study of an entropy dissipating finite volume scheme for a nonlocal cross-diffusion system - (preprint)
with Antoine Zurek - ESAIM: Mathematical Modelling and Numerical Analysis, 2023.
On a structure-preserving numerical method for fractional Fokker-Planck equations - (preprint)
with Nathalie Ayi, Hélène Hivert and Isabelle Tristani - Mathematics of Computation, 2023.
Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches - (preprint)
with C. Chainais-Hillairet, S. Lemaire and J. Moatti - Numerische Mathematik, 2022.
A Fokker-Planck approach to the study of robustness in gene expression - (preprint)
with Pierre Degond and Sepideh Mirrahimi - Mathematical Biosciences and Engineering, 2020.
Large time behavior of nonlinear finite volume schemes for convection-diffusion equations - (preprint)
with Clément Cancès, Claire Chainais-Hillairet and Stella Krell - SIAM Journal on Numerical Analysis, 2020.
A note on hypocoercivity for kinetic equations with heavy-tailed equilibrium - (full text)
with Nathalie Ayi, Hélène Hivert and Isabelle Tristani - Comptes Rendus, Mathématique, 2020.
Computation of sum of squares polynomials from data points - (preprint)
with Bruno Després - SIAM Journal on Numerical Analysis, 2020.
A projection algorithm on the set of polynomials with two bounds - (preprint)
with Martin Campos Pinto, Frédérique Charles and Bruno Després - Numerical Algorithms, 2020.
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations - (preprint)
with Marianne Bessemoulin-Chatard and Thomas Rey - Mathematics of Computation, 2019.
Large-time behavior of a family of finite volume schemes for boundary-driven convection-diffusion equations - (preprint)
with Claire Chainais-Hillairet - IMA Journal of Numerical Analysis, 2019.
Anisotropic Boltzmann-Gibbs dynamics of strongly magnetized Vlasov-Fokker-Planck equations - (preprint)
with L. Miguel Rodrigues - Kinetic and Related Models, 2019.
Large-time behavior of solutions to Vlasov-Poisson-Fokker-Planck equations: from evanescent collisions to diffusive limit - (preprint)
with L. Miguel Rodrigues - Journal of Statistical Physics, 2018.
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure - (preprint)
with Francis Filbet - Numerische Mathematik, 2017.
On massless electron limit for a multispecies kinetic system with external magnetic field - (preprint)
Journal of Differential Equations, 2016.
Finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion - (preprint)
with Clément Cancès and Annamaria Massimini - Finite Volumes for Complex Applications X - Volume 1, Elliptic and Parabolic Problems. FVCA 2023.
L∞ bounds for numerical solutions of noncoercive convection-diffusion equations - (preprint)
with C. Chainais-Hillairet - Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020.
Correction to: Polynomials with bounds and numerical analysis - (Erratum - Original paper here)
with Bruno Després - Numerical Algorithms, 2017.
Modelling and simulating a multispecies plasma - (Full text)
with Mehdi Badsi - ESAIM Proceedings, 2016.
Asymptotic and numerical analysis of kinetic and fluid models for the transport of charged particles - (Full text)
PhD Thesis, Université Lyon 1, 2017