01 / About me
About me
I am a full professor of Numerical Analysis at the Université de Montpellier, working on advanced numerical methods for partial differential equations.
02 / Research
Research
My research brings together numerical analysis, fluid and solid mechanics, and modern implementation techniques.
Numerical simulations
Examples computed with poly_rust. Select an image to enlarge it.
Lid-driven cavity flow
Velocity magnitude for a lid-driven cavity over an impermeable bedding.
Kirchhoff–Love plates
HHO solution of the four-point load Kirchhoff–Love problem on the finer mesh shown in the presentation.
3D magnetostatics
Vector-potential magnitude contours from a Discrete de Rham (DDR) magnetostatic simulation.
Selected recognitions
2024 Frontiers of Science Award in Mathematics for Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin methods.
Editorial activity
Associate Editor of Numerical Algorithms, Boletín de la Sociedad Matemática Mexicana, and Electronic Research Archive.
Selected press & interviews
NEMESIS: an ERC Synergy project · French
Portrait de l’UM · French
Talents CNRS · French
MaddMaths interview · Italian
Software
poly_rust ↗
A Rust library and external DSL for polytopal discretization methods.
HArDCore ↗
An HHO-oriented C++ library.
Publications 142
BibTeX ↓Research monographs2
- The Hybrid High-Order method for polytopal meshes: Design, analysis, and applications
- Mathematical aspects of discontinuous Galerkin methods
Edited monographs2
- Polyhedral Methods in Geosciences
- Numerical Methods for PDEs: State of the Art Techniques
Papers101
- A Reynolds-semi-robust H( div)-conforming method for unsteady incompressible non-Newtonian flowsNEMESIS
- A Hybrid High-Order method for fracture modelling
- A Hybrid High-Order method for the power-law Brinkman problem robust in all regimesNEMESIS
- Hybrid High-Order formulations with turbulence modelling capabilities for incompressible flow problemsNEMESIS
- Stability, convergence, and pressure-robustness of numerical schemes for incompressible flows with hybrid velocity and pressureNEMESIS
- Hyperelastic nature of the Hoek–Brown criterion
- Serendipity discrete complexes with enhanced regularityNEMESIS
- A Reynolds-semi-robust method with hybrid velocity and pressure for the unsteady incompressible Navier–Stokes equationsNEMESIS
- Homogeneous multigrid for hybrid discretizations: application to HHO methodsNEMESIS
- A discrete de Rham discretization of interface diffusion problems with application to the Leaky Dielectric ModelNEMESIS
- A Reynolds-semi-robust and pressure-robust Hybrid High-Order method for the time dependent incompressible Navier–Stokes equationsNEMESIS
- An exterior calculus framework for polytopal methodsNEMESIS
- Uniform Poincaré inequalities for the Discrete de Rham complex on general domainsNEMESIS
- A discrete three-dimensional divdiv complex on polyhedral meshes with application to a mixed formulation of the biharmonic problemNEMESIS
- A Péclet-robust discontinuous Galerkin method for nonlinear diffusion with advectionNEMESIS
- A pressure-robust HHO method for the solution of the incompressible Navier–Stokes equations on general meshes
- An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contactNEMESIS
- A pressure-robust Discrete de Rham scheme for the Navier–Stokes equationsNEMESIS
- An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem
- Cohomology of the discrete de Rham complex on domains of general topology
- A polytopal method for the Brinkman problem robust in all regimes
- An arbitrary-order discrete de Rham complex on polyhedral meshes: Exactness, Poincaré inequalities, and consistency
- Homological- and analytical-preserving serendipity framework for polytopal complexes, with application to the DDR method
- High-order multigrid strategies for HHO discretizations of elliptic equations
- A serendipity fully discrete div-div complex on polygonal meshes
- A fully discrete plates complex on polygonal meshes with application to the Kirchhoff–Love problem
- A Hybrid High-Order method for incompressible flows of non-Newtonian fluids with power-like convective behaviour
- Algebraic multigrid preconditioner for statically condensed systems arising from lowest-order hybrid discretizations
- A discrete de Rham method for the Reissner–Mindlin plate bending problem on polygonal meshes
- Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes
- A posteriori error estimates via equilibrated stress reconstructions for contact problems approximated by Nitsche's method
- A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of magnetostatics
- p-Multilevel preconditioners for HHO discretizations of the Stokes equations with static condensation
- An abstract analysis framework for monolithic discretisations of poroelasticity with application to Hybrid High-Order methods
- A Hybrid High-Order method for creeping flows of non-Newtonian fluids
- Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems
- An arbitrary-order method for magnetostatics on polyhedral meshes based on a discrete de Rham sequence
- Towards robust, fast solutions of elliptic equations on complex domains through HHO discretizations and non-nested multigrid methods
- An h-multigrid method for Hybrid High-Order discretizations
- Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods
- A Hybrid High-Order discretisation method for nonlinear poroelasticity
- A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces
- Fully discrete polynomial de Rham sequences of arbitrary degree on polygons and polyhedra
- A low-order nonconforming method for linear elasticity on general meshes
- A Hybrid High-Order method for the incompressible Navier–Stokes equations based on Temam's device
- A Hybrid High-Order method for passive transport in fractured porous media
- Preface: Special Issue on Model Reduction
- An advection-robust Hybrid High-Order method for the Oseen problem
- Unified formulation and analysis of mixed and primal discontinuous skeletal methods on polytopal meshes
- A Hybrid High-Order method for Kirchhoff–Love plate bending problems
- A Hybrid High-Order discretisation of the Brinkman problem robust in the Darcy and Stokes limits
- Assessment of Hybrid High-Order methods on curved meshes and comparison with discontinuous Galerkin methods
- A Hybrid High-Order method for Darcy flows in fractured porous media
- Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming
- Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes
- A third Strang lemma and an Aubin–Nitsche trick for schemes in fully discrete formulation
- A Hybrid High-Order method for the steady incompressible Navier–Stokes problem
- Weighted Interior Penalty discretization of fully nonlinear and weakly dispersive free surface shallow water flows
- An hp-Hybrid High-Order method for variable diffusion on general meshes
- A Hybrid High-Order method for nonlinear elasticity
- W^s,p-approximation properties of elliptic projectors on polynomial spaces, with application to the error analysis of a Hybrid High-Order discretisation of Leray–Lions problems
- A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes
- Arbitrary-order mixed methods for heterogeneous anisotropic diffusion on general meshes
- An arbitrary-order discontinuous skeletal method for solving electrostatics on general polyhedral meshes
- Stress and flux reconstruction in Biot's poro-elasticity problem with application to a posteriori error analysis
- A nonconforming high-order method for the Biot problem on general meshes
- A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form
- Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin methods
- A discontinuous skeletal method for the viscosity-dependent Stokes problem
- An a posteriori-driven adaptive Mixed High-Order method with application to electrostatics
- Hybridization of mixed high-order methods on general meshes and application to the Stokes equations
- Low-order reconstruction operators on polyhedral meshes: Application to Compatible Discrete Operator schemes
- A discontinuous-skeletal method for advection-diffusion-reaction on general meshes
- Equilibrated tractions for the Hybrid High-Order method
- Hybrid high-order methods for variable-diffusion problems on general meshes
- A hybrid high-order locking-free method for linear elasticity on general meshes
- An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow
- Adaptive regularization, linearization, discretization, and a posteriori error control for the two-phase Stefan problem
- An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
- A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
- An a posteriori-based, fully adaptive algorithm for thermal multiphase compositional flows in porous media with adaptive mesh refinement
- A review of recent advances in discretization methods, a posteriori error analysis, and adaptive algorithms for numerical modeling in geosciences
- A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes
- A locking-free discontinuous Galerkin method for linear elasticity in locally nearly incompressible heterogeneous media
- On the conservativity of cell centered Galerkin methods
- On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
- Analysis of a discontinuous Galerkin method for heterogeneous diffusion problems with low-regularity solutions
- Cell centered Galerkin methods for diffusive problems
- A pressure-correction scheme for convection-dominated incompressible flows with discontinuous velocity and continuous pressure
- A compact cell-centered Galerkin method with subgrid stabilization
- The G method for heterogeneous anisotropic diffusion on general meshes
- An abstract analysis framework for nonconforming approximations of diffusion problems on general meshes
- Discrete functional analysis tools for discontinuous Galerkin methods with application to the incompressible Navier–Stokes equations
- Cell centered Galerkin methods
- Expression template implementation of continuous and discontinuous Galerkin methods
- Discontinuous Galerkin methods for anisotropic semi-definite diffusion with advection
- An implicit high-order discontinuous Galerkin method for steady and unsteady incompressible flows
- Analysis of a discontinuous Galerkin approximation of the Stokes problem based on an artificial compressibility flux
- An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations
- Mass preserving finite element implementations of the level set method
- Comparison of four analytical and numerical models for a microchannel heat sink
Book chapters4
- A Hybrid High-Order method for multiple-network poroelasticity
- An introduction to recent developments in numerical methods for partial differential equations
- An introduction to Hybrid High-Order methods
- A review of Hybrid High-Order methods: formulations, computational aspects, comparison with other methods
Preprints11
- Analytical properties of polygonal Stokes and BGG Hessian complexes with application to Kirchhoff–Love platesNEMESIS
- poly_rust: a domain-specific language for polytopal methods with a Rust interpreterNEMESIS
- Optimal hp-error estimates and p-multigrid convergence for Hybrid High-Order discretizations of the Poisson equation
- Key challenges and bridges among convergence analysis techniques for polytopal methodsNEMESIS
- Hybrid methods for Friedrichs systems with application to scalar and vector diffusion-advection-reactionNEMESIS
- A Reynolds- and Hartmann-semirobust hybrid method for magnetohydrodynamicsNEMESIS
- A low-order hybrid method for the variable-density incompressible Navier–Stokes equationsNEMESIS
- Ghost stabilisation for cut finite element exterior calculusNEMESIS
- Conforming lifting and adjoint consistency for the Discrete de Rham complex of differential formsNEMESIS
- Design and homological analysis of twisted and BGG Stokes-de Rham complexes on polygonal meshesNEMESIS
- Uniform Poincaré inequalities for the discrete de Rham complex of differential formsNEMESIS
Proceedings20
- Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin methods: Summary
- A three-dimensional Hybrid High-Order method for magnetostatics
- A nonconforming high-order method for nonlinear poroelasticity
- A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form
- Benchmark session: The 2D Hybrid High-Order method
- Equilibrated stress reconstruction for linear elasticity problems with application to a posteriori error analysis
- Hybrid finite volume discretization of linear elasticity models on general meshes
- Lowest order methods for diffusive problems on general meshes: A unified approach to definition and implementation
- An a posteriori error estimator for a finite volume discretization of two-phase flow
- A comparison of last generation cell centered finite volume methods on challenging three dimensional problems
- Generalized L-scheme for the discretization of diffusion fluxes on general meshes
- A general framework for non-conforming approximations of the single phase Darcy equation
- The MPFA G scheme for heterogeneous anisotropic diffusion problems on general meshes
- A symmetric and coercive finite volume scheme for multiphase porous media flow with applications in the oil industry
- A symmetric finite volume scheme for anisotropic heterogeneous second-order elliptic problems
- A discontinuous Galerkin flux for anisotropic heterogeneous second-order elliptic problems
- Compact-stencil MPFA method for heterogeneous highly-anisotropic second order elliptic problems
- A high-order discontinuous Galerkin solver for 3D aerodynamic turbulent flows
- Analytical and numerical modeling of microchannel heat sinks
- Design of a microchannel cooling system for BTeV particle detector
Theses2
- Méthodes non conformes pour des équations aux dérivées partielles avec diffusion
- Discontinuous Galerkin methods for the incompressible Navier–Stokes equations
Publication statistics
Select a chart to enlarge it and view the underlying counts.
Publications per year 
Papers by journal 
Publications by year and type, including theses; excludes preprints. Timeline milestones: PhD (2006), HDR (2010).
View counts
| Year | Research monographs | Edited monographs | Papers | Book chapters | Proceedings | Theses | Total |
|---|---|---|---|---|---|---|---|
| 2002 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
| 2003 | 0 | 0 | 1 | 0 | 1 | 0 | 2 |
| 2004 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2005 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2006 | 0 | 0 | 2 | 0 | 1 | 1 | 4 |
| 2007 | 0 | 0 | 2 | 0 | 0 | 0 | 2 |
| 2008 | 0 | 0 | 1 | 0 | 7 | 0 | 8 |
| 2009 | 0 | 0 | 1 | 0 | 1 | 0 | 2 |
| 2010 | 0 | 0 | 4 | 0 | 0 | 1 | 5 |
| 2011 | 0 | 0 | 2 | 0 | 3 | 0 | 5 |
| 2012 | 1 | 0 | 3 | 0 | 0 | 0 | 4 |
| 2013 | 0 | 0 | 3 | 0 | 0 | 0 | 3 |
| 2014 | 0 | 0 | 4 | 0 | 0 | 0 | 4 |
| 2015 | 0 | 0 | 8 | 0 | 0 | 0 | 8 |
| 2016 | 0 | 0 | 5 | 1 | 0 | 0 | 6 |
| 2017 | 0 | 0 | 7 | 0 | 4 | 0 | 11 |
| 2018 | 0 | 1 | 11 | 2 | 0 | 0 | 14 |
| 2019 | 0 | 0 | 4 | 0 | 0 | 0 | 4 |
| 2020 | 1 | 0 | 4 | 0 | 1 | 0 | 6 |
| 2021 | 0 | 1 | 6 | 1 | 0 | 0 | 8 |
| 2022 | 0 | 0 | 5 | 0 | 0 | 0 | 5 |
| 2023 | 0 | 0 | 9 | 0 | 0 | 0 | 9 |
| 2024 | 0 | 0 | 7 | 0 | 1 | 0 | 8 |
| 2025 | 0 | 0 | 6 | 0 | 0 | 0 | 6 |
| 2026 | 0 | 0 | 6 | 0 | 0 | 0 | 6 |
Journal articles, including accepted and online-first papers.
View counts
| Category | Count |
|---|---|
| J. Comput. Phys. | 11 |
| Comput. Meth. Appl. Mech. Engrg. | 10 |
| ESAIM: Math. Model. Numer. Anal. | 7 |
| Comput. Math. Appl. | 6 |
| Math. Comp. | 6 |
| SIAM J. Numer. Anal. | 6 |
| C. R. Acad. Sci. Paris, Ser. I | 5 |
| IMA J. Numer. Anal. | 5 |
| Math. Models Methods Appl. Sci. | 5 |
| Calcolo | 4 |
| Comput. Meth. Appl. Math. | 4 |
| SIAM J. Sci. Comput. | 4 |
| J. Sci. Comput. | 3 |
| App. Num. Math. | 2 |
| Comp. & Fl. | 2 |
| Internat. J. Numer. Methods Engrg. | 2 |
| Numer. Meth. for PDEs | 2 |
| BIT Numerical Mathematics | 1 |
| Commun. Appl. Math. Comput. | 1 |
| Comp. Vis. in Sci. | 1 |
| Comptes Rendus Mécanique | 1 |
| Computer Aided Geometric Design | 1 |
| European Journal of Mechanics A/Solids | 1 |
| Found. Comput. Math. | 1 |
| IEEE Transactions on Magnetics | 1 |
| IJFV International Journal on Finite Volumes | 1 |
| Int. J. Geomath. | 1 |
| Int. J. Heat and Tech. | 1 |
| Int. J. Num. Meth. Fluids | 1 |
| J. Comput. Appl. Math. | 1 |
| J. Eur. Math. Soc. | 1 |
| Numer. Linear Algebra with Appl. | 1 |
| Oil & Gas Science and Technology | 1 |
| Results Appl. Math. | 1 |
Presentations 74
BibTeX ↓Presentations74
- Numerical approximation of partial differential equations on general meshesNEMESIS
- The Discrete de Rham methodNEMESIS
- Discrete de Rham methodsNEMESIS
- From Finite Elements to Hybrid High-Order methodsNEMESIS
- From Finite Elements to Hybrid High-Order methodsNEMESIS
- Polytopal approximations of the de Rham complexNEMESIS
- Polytopal Exterior CalculusNEMESIS
- A new generation of numerical methods for partial differential equations: The NEMESIS projectNEMESIS
- Polytopal approximations of Hilbert complexesNEMESIS
- Hybrid High-Order methods: Convergence analysis and flux formulationNEMESIS
- Basic principles of polytopal approximations of partial differential equationsNEMESIS
- Hybrid High-Order methods: Introduction and fully discrete analysis frameworkNEMESIS
- An introduction to Discrete de Rham (DDR) methodsNEMESIS
- Approssimazione numerica di sistemi fisiciNEMESIS
- An introduction to Discrete de Rham (DDR) methodsNEMESIS
- An introduction to Discrete de Rham (DDR) methods
- An introduction to Discrete de Rham (DDR) methods
- Discrete de Rham (DDR) methods for continuum mechanics
- Discrete de Rham methods for mixed formulations
- Discrete de Rham (DDR) complexes for compatible approximations of physical problems on general meshes
- An introduction to discrete de Rham methods. A polytopal exterior calculus framework
- Hybrid High-Order methods for the incompressible Navier–Stokes equations
- A Hybrid High-Order method for the incompressible Navier–Stokes problem robust for large irrotational body forces
- From physical models to advanced numerical methods through de Rham cohomology
- From physical models to advanced numerical methods through de Rham cohomology
- Hybrid High-Order methods for Darcean flows in complex porous media
- A discrete exact grad-curl-div complex on generic polyhedral meshes. Part I: Algebraic properties
- Arbitrary-order fully discrete complexes on polyhedral meshes
- Fully discrete polynomial de Rham complexes on polyhedral meshes with application to magnetostatics
- Hybrid High-Order methods for nonlinear problems
- Hybrid High-Order methods for nonlinear problems
- Fully discrete polynomial de Rham complexes on polyhedral meshes with application to magnetostatics
- Recent advances on fully discrete methods for polyhedral meshes
- An arbitrary-order discrete de Rham complex on polyhedral meshes
- Fully discrete polynomial de Rham sequences of arbitrary degree on polyhedral meshes
- Fully discrete polynomial de Rham sequences of arbitrary degree on polyhedral meshes
- Hybrid High-Order methods for poroelasticity
- Hybrid High-Order methods for poroelasticity
- Recent advances on Hybrid High-Order methods for problems in incompressible fluid mechanics
- Hybrid High-Order methods for diffusion problems on polytopes and curved elements
- An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics
- Hybrid High-Order methods for elasticity
- An introduction to Hybrid High-Order methods with applications to incompressible fluid mechanics
- A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device
- A Hybrid High-Order method for incompressible Navier–Stokes equations based on Temam's device
- An introduction to Hybrid High-Order methods with application to the incompressible Navier–Stokes equations
- A non-standard application of the Raviart–Thomas–Nédélec element: A HHO method for the Brinkman problem robust in the Darcy and Stokes limits
- An introduction to the convergence analysis of discretisation methods for PDEs with application to Hybrid High-Order methods
- An introduction to Hybrid High-Order methods
- An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity
- An introduction to Hybrid High-Order methods - Nonlinear elasticity and poroelasticity
- Recent advances on Hybrid High-Order methods for linear and nonlinear problems
- Recent advances on Hybrid High-Order methods for nonlinear problems
- Hybrid High-Order methods
- A Hybrid High-Order method for Leray–Lions equations
- Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods
- Hybrid High-Order methods on general meshes
- An a posteriori-based fully adaptive algorithm for the two-phase Stefan problem
- A Hybrid High-Order method for locally degenerate advection-diffusion-reaction
- An introduction to Hybrid High-Order methods
- Hybrid High-Order (HHO) methods on general meshes
- Hybrid and mixed high-order methods
- Hybrid High-Order methods for degenerate advection-diffusion-reaction
- Hybrid high-order methods for quasi-incompressible linear elasticity on general meshes
- A family of arbitrary-order mixed methods for anisotropic heterogeneous diffusion
- A posteriori error estimates, stopping criteria, and adaptivity for multiphase compositional Darcy flows in porous media
- Discontinuous Galerkin methods and applications
- An extension of the Crouzeix–Raviart and Raviart–Thomas spaces to general meshes
- A hybrid finite volume generalization of the Crouzeix-Raviart element
- Locking-free numerical approximations of the elasticity operator
- Cell centered Galerkin methods for diffusive problems on general meshes
- Recent advances on nonconforming methods for diffusive problems on general meshes
- Lowest order methods for diffusive problems on general meshes
- Nonconforming methods for PDEs with diffusion
03 / Teaching
Teaching
Courses at the Faculté des Sciences, Département de Mathématiques.
Master Modélisation et Analyse Numérique ↗
Course resources
Analyse Numérique 4
The Hybrid High-Order method for polytopal meshes — HAL