Publications

83 articles · also on Google Scholar, arXiv and ORCID

Themes

Quantum mechanics: Analysis and approximation of quantum Boltzmann and von Neumann equations.
Plasma physics: Vlasov–Poisson system with or without a strong magnetic field; Fokker–Planck and Landau equations for collisions.
Rarefied gases: Boltzmann, ES-BGK and BGK equations.
Life sciences: Coagulation–fragmentation, Keller–Segel system, neuroscience models.
Numerical analysis: Entropy methods, discrete functional inequalities.

Research software: HOPE, a C++ library for kinetic equations.

Preprints

Discrete hypocoercive estimates for discontinuous Galerkin methods: application to the Vlasov-Poisson-Fokker-Planck system preprint (2026), with Y. Cai, A. Blaustein and T. Xiong. Plasma physics arXiv
Convergence analysis of a Crank-Nicolson scheme for strongly magnetized plasmas preprint (2026), with L. M. Rodrigues and K.-H. Trinh. Plasma physics arXiv
A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system preprint (2025), with A. Blaustein, G. Dimarco and M.-H. Vignal. Plasma physics arXiv

2026

Numerical analysis of the homogeneous Landau equation: approximation, error estimates and simulation Numer. Math. (2026), with Y. Gui and L.-B. He. Plasma physics arXiv
On the approximation of the von Neumann equation in the semi-classical limit. Part II : numerical analysis Math. Comp. (2026), with F. Golse. Quantum mechanics arXiv
Trend to equilibrium and diffusion limit for the inertial Kuramoto-Sakaguchi equation SIAM J. Math. Anal. (2026), with M. Kang. Life sciences arXiv
A modified Crank-Nicolson scheme for the Vlasov-Poisson system with a strong external magnetic field J. Comput. Phys. 552 (2026), Paper No. 114693, 26 pp., with L. M. Rodrigues and K.-H. Trinh. Plasma physics arXiv

2025

On the approximation of the von-Neumann equation in the semi-classical limit. Part I: Numerical algorithm J. Comput. Phys. 527 (2025), Paper No. 113810, 20 pp., with F. Golse. Quantum mechanics arXiv

2024

A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model J. Comput. Phys. 498 (2024), with A. Blaustein. Plasma physics arXiv
On a discrete framework of hypocoercivity for kinetic equations Math. Comp. 93 (2024), with A. Blaustein. Plasma physics arXiv

2023

On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system SIAM J. Numer. Anal. (2023), no. 5, with M. Bessemoulin-Chatard. Plasma physics arXiv
Asymptotically preserving particle methods for strongly magnetized plasmas in a torus J. Comput. Phys. 480 (2023), Paper No. 112015, with L. M. Rodrigues. Plasma physics arXiv
Concentration phenomena in Fitzhugh-Nagumo's equations: a mesoscopic approach SIAM J. Math. Anal. 55 (2023), no. 1, 367–404, with A. Blaustein. Life sciences arXiv

2022

Fokker-Planck multi-species equations in the adiabatic asymptotics J. Comput. Phys. 471 (2022), Paper No. 111642, 28 pp., with C. Negulescu. Plasma physics arXiv
On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system J. Comput. Phys. 451 (2022), with M. Bessemoulin-Chatard. Plasma physics arXiv
Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System Commun. Appl. Math. Comput. 4 (2022), with T. Xiong. Plasma physics arXiv

2021

Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas Numer. Math. 149 (2021), with L. M. Rodrigues and H. Zakerzadeh. Plasma physics arXiv
Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions BIT Numer. Math. (2021), with J. Crevat. Life sciences arXiv

2020

Asymptotics of the three-dimensional Vlasov equation in the large magnetic field limit J. Éc. polytech. Math. 7 (2020), 1009–1067, with L. M. Rodrigues. Plasma physics arXiv
Convergence of a finite volume scheme for a system of interacting species with cross-diffusion Numer. Math. 145 (2020), no. 3, 473–511, with J. A. Carrillo and M. Schmidtchen. Life sciences arXiv

2019

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system SIAM J. Math. Anal. 51 (2019), no. 1, 346–373, with J. Crevat and G. Faye. Life sciences arXiv

2018

A hybrid discontinuous Galerkin scheme for multi-scale kinetic equations J. Comput. Phys. 372 (2018), 841–863, with T. Xiong. Rarefied gases arXiv
On the Vlasov-Maxwell system with a strong magnetic field SIAM J. Appl. Math. 78 (2018), no. 2, 1030–1055, with T. Xiong and E. Sonnendrücker. Plasma physics PDF
A p-adaptive local discontinuous Galerkin level set method for Willmore flow J. Sci. Comput. 76 (2018), no. 2, 1148–1167, with R. Guo. Numerical analysis arXiv
Discontinuous Galerkin methods for a kinetic model of self-organized dynamics Math. Models Methods Appl. Sci. 28 (2018), no. 6, 1171–1197, with C.-W. Shu. Life sciences arXiv

2017

Asymptotically preserving Particle-In-Cell methods for inhomogeneous strongly magnetized plasmas SIAM J. Numer. Anal. 55 (2017), no. 5, 2416–2443, with L. M. Rodrigues. Plasma physics arXiv
On a three dimensional vision based collision avoidance model J. Stat. Phys. 168 (2017), no. 3, 680–706, with C. Parzani. Life sciences arXiv
A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure Numer. Math. 137 (2017), no. 3, 535–577, with M. Herda. Numerical analysis arXiv

2016

On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation J. Stat. Phys. 165 (2016), no. 4, 765–784, with P. Degond. Plasma physics arXiv
Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs J. Sci. Comput. 68 (2016), no. 3, 1029–1054, with R. Guo and Y. Xu. Numerical analysis PDF
Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field SIAM J. Numer. Anal. 54 (2016), no. 2, 1120–1146, with L. M. Rodrigues. Plasma physics arXiv
High order time discretization for backward semi-Lagrangian methods J. Comput. Appl. Math. 303 (2016), 171–188, with C. Prouveur. Plasma physics PDF
High order semi-Implicit schemes for time dependent partial differential equations J. Sci. Comput. 68 (2016), no. 3, 975–1001, with S. Boscarino and G. Russo. Numerical analysis PDF

2015

On steady-state preserving spectral methods for homogeneous Boltzmann equations C. R. Math. Acad. Sci. Paris 353 (2015), no. 4, 309–314, with L. Pareschi and T. Rey. Rarefied gases arXiv
A hierarchy of hybrid numerical methods for multi-scale kinetic equations SIAM J. Sci. Comput. 37 (2015), no. 3, A1218–A1247, with T. Rey. Rarefied gases arXiv
On discrete functional inequalities for some finite volume schemes IMA J. Numer. Anal. 35 (2015), no. 3, 1125–1149, with M. Bessemoulin-Chatard and C. Chainais-Hillairet. Numerical analysis arXiv

2014

Conservative and non-conservative methods based on Hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations J. Comput. Phys. 279 (2014), 18–36, with C. Yang. Plasma physics arXiv
Numerical Simulations of Kinetic Models for chemotaxis SIAM J. Sci. Comput. 36 (2014), no. 3, B348–B366, with C. Yang. Life sciences arXiv

2013

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems ESAIM Math. Model. Numer. Anal. 47 (2013), no. 2, 609–633, with A. Rambaud. Rarefied gases arXiv
Inverse Lax-Wendroff methods for boundary conditions of Boltzmann type models J. Comput. Phys. 245 (2013), 43–61, with C. Yang. Rarefied gases arXiv
A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media J. Comput. Phys. 248 (2013), 177–199, with Th. Rey. Rarefied gases arXiv

2012

A finite volume scheme for nonlinear degenerate parabolic equations SIAM J. Sci. Comput. 34 (2012), no. 5, B559–B583, with M. Bessemoulin-Chatard. Numerical analysis arXiv
On deterministic approximation of the Boltzmann equation in a bounded domain Multiscale Model. Simul. 10 (2012), no. 3, 792–817. Rarefied gases arXiv
Numerical study of a nonlinear heat equation for plasma physics Int. J. Comput. Math. 89 (2012), no. 8, 1060–1082, with C. Negulescu and C. Yang. Plasma physics arXiv
A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime ESAIM Math. Model. Numer. Anal. 46 (2012), no. 2, 443–463, with J. Hu and S. Jin. Quantum mechanics arXiv
Analysis of a High Order Finite Volume Scheme for the Vlasov-Poisson System Discrete Contin. Dyn. Syst. Ser. S 5 (2012), no. 2, 283–305, with R. Duclous and B. Dubroca. Plasma physics PDF

2011

An Asymptotic Preserving Scheme for the ES-BGK model of the Boltzmann equation J. Sci. Comput. 46 (2011), no. 2, 204–224, with S. Jin. Rarefied gases arXiv
Analysis of spectral methods for the homogeneous Boltzmann equation Trans. Amer. Math. Soc. 363 (2011), no. 4, 1947–1980, with C. Mouhot. Rarefied gases arXiv

2010

A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources J. Comput. Phys. 229 (2010), no. 20, 7625–7648, with S. Jin. Rarefied gases arXiv

2009

High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications J. Comput. Phys. 228 (2009), no. 14, 5072–5100, with R. Duclous, B. Dubroca and V. Tikhonchuk. Plasma physics arXiv
Semi-lagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics Kinet. Relat. Models 2 (2009), no. 1, 231–250, with G. Russo. Rarefied gases PDF

2008

An Asymptotically Stable Scheme for Diffusive Coagulation-Fragmentation Models Commun. Math. Sci. 6 (2008), no. 2, 257–280. Life sciences arXiv
Convergence of a Finite Volume Scheme for the Coagulation-Fragmentation Equations Math. Comp. 77 (2008), no. 262, 851–882, with J.-P. Bourgade. Life sciences PDF

2007

Asymptotic Behavior of a Finite Volume Scheme for the Transient Drift-Diffusion Model IMA J. Numer. Anal. 27 (2007), no. 4, 689–716, with C. Chainais-Hillairet. Numerical analysis PDF

2006

A Finite Volume Scheme for the Patlak-Keller-Segel Chemotaxis Model Numer. Math. 104 (2006), no. 4, 457–488. Life sciences PDF
Solving the Boltzmann Equation in N log(N) with Deterministic Methods SIAM J. Sci. Comput. 28 (2006), no. 3, 1029–1053, with C. Mouhot and L. Pareschi. Rarefied gases arXiv
Modeling and Numerical Simulation of Space Charge Dominated Beams in the Paraxial Approximation Math. Models Methods Appl. Sci. 16 (2006), no. 5, 763–791, with E. Sonnendrücker. Plasma physics PDF
A rescaling velocity method for kinetic equations: I. homogeneous case In: Modelling and numerics of kinetic dissipative systems, 191–202, Nova Science Publishers, Hauppauge, NY (2006), with G. Russo. Rarefied gases PDF

2005

Approximation of Hyperbolic Models for Chemosensitive Movement SIAM J. Sci. Comput. 27 (2005), no. 3, 850–872, with C.-W. Shu. Life sciences PDF
Derivation of Hyperbolic Models for Chemosensitive Movement J. Math. Biol. 50 (2005), no. 2, 189–207, with Ph. Laurençot and B. Perthame. Life sciences PDF
Analysis of the Reduced Vlasov-Maxwell Model with Boundary Conditions Quart. Appl. Math. 63 (2005), no. 4, 691–714, with Y. Guo and C.-W. Shu. Plasma physics PDF
A conservative and entropic method for the Vlasov-Fokker-Planck-Landau equation In: Numerical methods for hyperbolic and kinetic problems, 59–70, IRMA Lect. Math. Theor. Phys. 7, EMS, Zürich (2005), with N. Crouseilles. Plasma physics PDF
Accurate numerical methods for the collisional motion of (heated) granular flows J. Comput. Phys. 202 (2005), no. 1, 216–235, with L. Pareschi and G. Toscani. Rarefied gases

2004

Numerical Approximation of Collisional Plasma by High Order Methods J. Comput. Phys. 201 (2004), no. 2, 546–572, with N. Crouseilles. Plasma physics PDF
Vlasov Simulations of Beams by a Moving Grid Comput. Phys. Communications, vol. 164 no. 1-3, (2004), pp. 390–395, with E. Sonnendrücker, E. Oudet, A. Friedman and J.-L. Vay. Plasma physics PDF
Mass Conserving Solutions and Non Conserving Approximation to the Smoluchowski Coagulation Equation Arch. Math. (Basel) 83 (2004), no. 6, 558–567, with Ph. Laurençot. Life sciences PDF
Numerical Simulation of the Smoluchowski Coagulation Equation SIAM J. Sci. Comput. 25 (2004), no. 6, 2004–2028, with Ph. Laurençot. Life sciences PDF
Accurate numerical methods for the Boltzmann equation In: Modeling and computational methods for kinetic equations, 117–145, Model. Simul. Sci. Eng. Technol., Birkhäuser, Boston (2004), with G. Russo. Rarefied gases

2003

High order Numerical Methods for the Space Non Homogeneous Boltzmann Equation J. Comput. Phys. 186 (2003), no. 2, 457–480, with G. Russo. Rarefied gases PDF
Numerical Approximation of the Lifschitz-Slyozov-Wagner Equation SIAM J. Numer. Anal. 41 (2003), no. 2, 563–588, with Ph. Laurençot. Life sciences PDF
Global Existence for the Vlasov-Darwin System in R3 for Small Initial Data Math. Methods Appl. Sci. 26 (2003), no. 4, 297–319, with S. Benachour, Ph. Laurençot and E. Sonnendrücker. Plasma physics PDF
An adaptive numerical method for the Vlasov equation based on a multiresolution analysis In: Numerical mathematics and advanced applications, 437–446, Springer, Milan (2003), with N. Besse, M. Gutnic, I. Paun and E. Sonnendrücker. Plasma physics arXiv
Numerical Methods for the Vlasov Equation In: Numerical mathematics and advanced applications, 459–468, Springer, Milan (2003), with E. Sonnendrücker. Plasma physics
Comparison of Eulerian Vlasov solvers Comput. Phys. Comm. 150 (2003), no. 3, 247–266, with E. Sonnendrücker. Plasma physics
Numerical solution of the Fokker-Planck-Landau equation by spectral methods Commun. Math. Sci. 1 (2003), no. 1, 206–207, with L. Pareschi. Plasma physics

2002

A Numerical Method for the Accurate Solution of the Fokker-Planck-Landau Equation in the Non Homogeneous Case J. Comput. Phys. 179 (2002), no. 1, 1–26, with L. Pareschi. Plasma physics PDF
Direct Axisymmetric Vlasov Simulations of Space Charged Dominated Beams In: Computational science—ICCS 2002, Part III, 305–314, Lecture Notes in Comput. Sci. 2331, Springer, Berlin (2002), with E. Sonnendrücker and J.-L. Lemaire. Plasma physics PDF
Parallelization of a Vlasov Solver by Communication Overlapping Proceedings PDPTA 2002 (2002), with E. Violard. Plasma physics PDF
Numerical Solution of the Non Homogeneous Fokker-Planck-Landau Equation In: Progress in industrial mathematics at ECMI 2000, 325–331, Math. Ind. 1, Springer, Berlin (2002), with L. Pareschi. Plasma physics

2001

Convergence of a Finite Volume Scheme for the One Dimensional Vlasov-Poisson System SIAM J. Numer. Anal. 39 (2001), no. 4, 1146–1169. Plasma physics PDF
Conservative Numerical Schemes for the Vlasov Equation J. Comput. Phys. 172 (2001), no. 1, 166–187, with E. Sonnendrücker and P. Bertrand. Plasma physics PDF

2000

Convergence d'un schéma de type volumes finis pour la résolution numérique du système de Vlasov-Poisson en dimension un C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 11, 979–984. Plasma physics

1999

Comparison of Numerical Schemes for Fokker-Planck-Landau Equation In: CEMRACS 1999 (Orsay), 161–181, ESAIM Proc. 10, SMAI, Paris (1999), with C. Buet and S. Cordier. Plasma physics PDF