Francis Filbet's publication page

On the approximation of the von Neumann equation in the semi-classical limit. Part II : numerical analysis, preprint (2025), with F. Golse.

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.

On the approximation of the von Neumann equation in the semi-classical limit. Part I : numerical algorithm, J. Comp. Physics, 527 (2025), with F. Golse.

Trend to equilibrium and diffusion limit for the inertial Kuramoto-Sakaguchi equation, preprint (2023), with M. Kang.

A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model, J. Comput. Physics, 498 (2024), with A. Blaustein.

On a discrete framework of hypocoercivity for kinetic equations, Mathematics of Computation, 93 (2024), with A. Blaustein.

On the convergence of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system, SIAM J. Numer. Analysis (2023), no. 5, with M. Bessemoulin-Chatard.

Asymptotically preserving particle methods for strongly magnetized plasmas in a torus, J. Comput. Physics, vol. 480 (2023) #112015, with L. M. Rodrigues.

Concentration phenomena in Fitzhugh-Nagumo's equations: a mesoscopic approach, SIAM J. Math. Anal. 55 (2023), no. 1, 367–404, with A. Blaustein.

Fokker-Planck multi-species equations in the adiabatic asymptotics, J. Comput. Phys. 471 (2022), Paper No. 111642, 28 pp, with C. Negulescu.

On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system, J. Comput. Phys. 451 (2022), with M. Bessemoulin-Chatard.

Conservative discontinuous Galerkin/Hermite Spectral Method for the Vlasov-Poisson System, Commun. Appl. Math. Comput. 4 (2022), with T. Xiong.

Convergence Analysis of Asymptotic Preserving Schemes for Strongly Magnetized plasmas, Numer. Math. 149 (2021), with L. M. Rodrigues and H. Zakerzadeh.

Asymptotic preserving schemes for the FitzHugh-Nagumo transport equation with strong local interactions, BIT Numerical Algorithm, (2021), with J. Crevat.

Asymptotics of the three dimensional Vlasov equation in the large magnetic field limit, Journal Ecole Polytechnique, Tome 7, (2020), pp. 1009-1067, with L. M. Rodrigues.

Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion, Numerische Mathematik, 145 (2020), pp. 473-511, with J. A. Carrillo and M. Schmidtchen.

Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system, SIAM J. Math. Analysis, 51 (2019), pp. 346–373, with J. Crevat and G. Faye.

A hybrid discontinuous Galerkin scheme for multi-scale kinetic equations, J. Comput. Physics, 372 (2018), pp. 841–863, with T. Xiong.

On the Vlasov-Maxwell system with a strong magnetic field SIAM J. Applied Mathematics, vol 78, (2018), pp. 1030-1055, with T. Xiong and E. Sonnendrücker.

A p-adaptive local discontinuous Galerkin level set method for Willmore flow, J. Sci. Computing, 76 (2018), no. 2, pp. 1148–1167, with R. Guo.

Discontinuous Galerkin methods for a kinetic model of self-organized dynamics, Math. Meth. Model. Applied Sciences, 28, no. 6 (2018), pp. 1171–1197, with C. W. Shu.

Asymptotically preserving Particle-In-Cell methods for inhomogeneous stongly magnetized plasmas, SIAM J. Numer. Analysis, 55 (2017), no. 5, pp. 2416–2443, with L. M. Rodrigues.

On a three dimensional vision based collision avoidance model, J. Stat Physics, vol. 168, (2017) pp. 680-716, with C. Parzani.

A finite volume scheme for boundary-driven convection-diffusion equations with relative entropy structure, Numerische Mathematik, 137 (2017), no. 3, pp. 535–577, with M. Herda.

On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation. J. Stat. Physics, vol. 165 (2016), pp. 765--784, with P. Degond.

Efficient high order semi-implicit time discretization and local discontinuous Galerkin methods for highly nonlinear PDEs, J. Sci. Computing, 68 (2016), no. 3, pp. 1029–1054, with R. Guo and Y. Xu.

Asymptotically stable particle-in-cell methods for the Vlasov-Poisson system with a strong external magnetic field, SIAM J. Numer. Analysis, vol. 54 (2016), pp. 1120-1146, with L. M. Rodrigues.

High order time discretization for backward semi-Lagrangian methods, Journal of Computational and Applied Mathematics, vol 303, (2016) pp. 171–188, with C. Prouveur.

On steady-state preserving spectral methods for homogeneous Boltzmann equations, Comptes Rendus Mathematiques, vol. 353, issue: 4 (2015), pp. 309-314, with L. Pareschi and T. Rey.

A hierarchy of hybrid numerical methods for multi-scale kinetic equations, SIAM J. Sci. Computing, 37 issue 3, pp. A1218-A1247 (2015), with T. Rey.

High order semi-Implicit schemes for time dependent partial differential equations, J. Sci. Comput. 68 (2016), no. 3, pp. 975–1001, with S. Boscarino and G. Russo.

On discrete functional inequalities for some finite volume schemes, IMA J. Num. Analysis, 35 no. 3 (2015), pp. 1125–-1149, with M. Bessemoulin-Chatard and C. Chainais-Hillairet.

Conservative and non-conservative methods based on Hermite weighted essentially-non-oscillatory reconstruction for Vlasov equations, J. Comput. Physics, vol. 279 (2014) pp. 18-36, with C. Yang.

Numerical Simulations of Kinetic Models for chemotaxis, SIAM J. Scientific Computing, vol. 36, no. 3 (2014), with C. Yang.

Analysis of an Asymptotic Preserving Scheme for Relaxation Systems, ESAIM - Math. Mod. Num. Anal. vol. 47 (2013), pp. 609--633, with A Rambaud.

Inverse Lax-Wendroff methods for boundary conditions of Boltzmann type models, J. Comput. Physics, vol 245, pp. 43-61 (2013) with C. Yang.

A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media., J. Comput. Physics, vol 248, pp. 177-199 (2013) with Th. Rey.

A finite volume scheme for nonlinear degenerate parabolic equations, SIAM J. Scientific Computing, vol. 34, no. 5 (2012), pp. 559--583, with M. Bessemoulin-Chatard.

On deterministic approximation of the Boltzmann equation in a bounded domain, Multiscale Modeling and Simulation vol 10 issue 3 (2012), pp. 792--817.

Numerical study of a nonlinear heat equation for plasma physics, International Journal of Computer Mathematics vol. 89 issue 8 (2012), pp. 1060--1082, with C. Negulescu and C. Yang.

A Numerical Scheme for the Quantum Boltzmann Equation Efficient in the Fluid Regime, ESAIM - Math. Mod. Num. Anal. vol. 46 (2012), pp. 443--463, with J. Hu and S. Jin.

Analysis of a High Order Finite Volume Scheme for the Vlasov-Poisson System, DCDS-S, vol. 5 (2012), pp. 283--305, with R. Duclous and B. Dubroca.

An Asymptotic Preserving Scheme for the ES-BGK model pof the Boltzmann equation, J. Sci. Computing, vol. 46, Number 2 (2011), pp. 204-224, with S. Jin.

A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources, J. Comp. Phys. vol. 229 no 20, (2010), pp. 7625-7648, with S. Jin.

High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications, J. Comput. Phys, vol. 228, no 14 (2009), pp. 5072-5100, with R. Duclous, B. Dubroca and V. Tikhonchuk.

Semi-lagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics. Kin. and Related Models, vol. 2 no. 1, (2009), pp. 231--250, with G. Russo.

An Asymptotically Stable Scheme for Diffusive Coagulation-Fragmentation Models, Comm. Math. Sciences vol 6 no. 2 (2008), pp. 257--280.

Convergence of a Finite Volume Scheme for the Coagulation-Fragmentation Equations, Maths. Comp. vol. 77, (2008), pp. 851--882, with J.-P. Bourgade.

Asymptotic Behavior of a Finite Volume Scheme for the Transient Drift-Diffusion Model, IMA J. Num. Anal. vol. 27 no. 4, (2007), pp. 689--716. with C. Chainais-Hillairet

A Finite Volume Scheme for the Patlak-Keller-Segel Chemotaxis Model, Numerische Mathematik, vol. 104, (2006), pp. 457--488.

Solving the Boltzmann Equation in N log(N) with Deterministic Methods, SIAM J. Scientific Computing, vol. 28 no. 3, (2006), pp. 1029--1053, with C. Mouhot and L. Pareschi.

Modeling and Numerical Simulation of Space Charge Dominated Beams in the Paraxial Approximation, Mathematical Models and Methods in the Applied Sciences, vol. 16 no. 5, (2006) pp. 763--791, with E. Sonnendrücker.

Approximation of Hyperbolic Models for Chemosensitive Movement, SIAM J. Scientific Computing, vol. 27 no. 3, (2005), pp. 850--872, with C.-W. Shu.

Derivation of Hyperbolic Models for Chemosensitive Movement, J. Math. Biology, vol. 50 (2005) no. 2, pp. 189--207, with Ph. Laurencot and B. Perthame.

Analysis of the Reduced Vlasov-Maxwell Model with Boundary Conditions, Quarterly Applied Math., vol. 63 no 4, (2005) pp. 691-714, with Y. Guo and C.-W. Shu

A conservative and entropic method for the Vlasov-Fokker-Planck-Landau equation, Numerical Methods for Hyperbolic and Kinetic Problems, IRMA Lectures in Mathematics and Theoretical Physics with N. Crouseilles.

Numerical Approximation of Collisional Plasma by High Order Methods, J. Comput. Physics, vol. 201 no. 2, (2004), pp. 546--572, with N. Crouseilles.

Vlasov Simulations of Beams by a Moving Grid, Comput. Phys. Communications, vol. 164 no. 1-3, (2004), pp. 390--395, with E. Sonnendrucker, E. Oudet, A. Friedman and J.-L. Vay.

Mass Conserving Solutions and Non Conserving Approximation to the Smoluchowski Coagulation Equation, Archiv der Mathematik, vol. 83 no. 6, (2004), pp. 558--567 with Ph. Laurencot.

A rescaling velocity method for kinetic equations: I. homogeneous case, Proceedings Modelling and Numerics of Kinetic Dissipative Systems, Lipari, Italy, 2004, Nova-Science with G. Russo

Numerical Simulation of the Smoluchowski Coagulation Equation, SIAM J. of Scientific Computing, vol. 25 no. 6, (2004), pp. 2004-2028 with Ph. Laurencot.

High order Numerical Methods for the Space Non Homogeneous Boltzmann Equation, J. Comput. Physics, vol. 186 no. 2, (2003), pp. 457--480, with G. Russo

Numerical Approximation of the Lifschitz-Slyozov-Wagner Equation, SIAM J. Numer. Analysis, 41 no. 2, (2003), pp. 563--588, with Ph. Laurencot

Global Existence for the Vlasov-Darwin System in R3 for Small Initial Data, Math. Methods Appl. Sciences, vol. 26 no. 4 (2003), pp. 297--319, with S. Benachour, Ph. Laurencot and E. Sonnendrücker.

A Numerical Method for the Accurate Solution of the Fokker-Planck-Landau Equation in the Non Homogeneous Case, J. Comput. Physics vol. 179 no. 1, (2002), pp. 1--26, with L. Pareschi.

Direct Axisymmetric Vlasov Simulations of Space Charged Dominated Beams, Lecture Notes in Computer Sciences, ICCS 2002, part 3, (2002) 305--314, with E. Sonnendrucker and J.-L. Lemaire.

Parallelization of a Vlasov Solver by Communication Overlapping, Proceedings PDPTA 2002 (2002), with E. Violard.

An adaptive numerical method for the Vlasov equation based on a multiresolution analysis, Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer pp. 437--446 (2003) with N. Besse, M. Gutnic, I. Paun and E. Sonnendrücker.

Numerical Methods for the Vlasov Equation, Brezzi, Franco (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2001, the 4th European conference, Ischia, July 2001. Berlin: Springer pp. 459--468 (2003), with E. Sonnendrücker.

Convergence of a Finite Volume Scheme for the One Dimensional Vlasov-Poisson System, SIAM J. Numer. Analysis, vol. 39 no. 4, (2001), pp. 1146--1169

Conservative Numerical Schemes for the Vlasov Equation, J. Comput. Physics 172 no. 1, (2001), pp. 166--187, with E. Sonnendrucker and P. Bertrand.

Numerical Solution of the Non Homogeneous Fokker-Planck-Landau Equation, Mathematics in Industry, vol. 1: Anile, A.M.; Capasso, V.; Greco, A., (Eds.) Progress in Industrial Mathematics at ECMI 2000 (Springer), 325--331 (2000), with L. Pareschi.

Convergence d'un schéma de type volumes finis pour le système de Vlasov-Poisson, Comptes Rendus Mathématiques 330, série I Mathématique pp. 979--984 (2000)

Comparison of Numerical Schemes for Fokker-Planck-Landau Equation, ESAIM Proceedings, vol. 10, Soc. Math. Appl. Industry, Paris, (1999); pp. 161--181, with C. Buet and S. Cordier.

Francis FILBET

Publications

Quantum mechanics :

Plasma physics :

Rarefied gas dynamics :

Life sciences :

Miscellaneous :