Florent CHAVE

CNRS postdoctoral fellow in Applied Mathematics
Côte d'Azur University, mathematics lab. J. A. Dieudonné
E-mail: florent.chave univ-cotedazur.fr
Curriculum vitæ: cv.pdf ()

Keywords: Numerical analysis, mathematical modeling,
scientific computing
Research interest: arbitrary-order polyhedral methods
for PDEs, a priori error analysis, coupled PDEs
with high-dimensionality gap, porous media
flows, electromagnetism, phase-field modeling

Vitæ
Since 10/2020 — CNRS postdoctoral fellow within the PDEs and Numerical Analysis group "ANEDP" at the mathematics
department J. A. Dieudonné of the Côte d'Azur University, France
Member of the team-project COFFEE at Inria Sophia Antipolis - Méditerranée, France
Part of an European project (EURAD) that aims to mobilize academic research on major nuclear-related issues
Working on the coupling of non-isothermal compositional liquid gas Darcy and free gas flows
In collaboration with R. Masson and K. Brenner
12/18-07/20 — Inria postdoctoral fellow within the team-project RAPSODI at Inria Lille - Nord Europe, France
Member of the Numerical Analysis and PDEs group "ANEDP" at the mathematics department Paul Painlevé of the
University of Lille, France
Working on high-order polyhedral discretization methods for electromagnetism
In collaboration with S. Lemaire
09/15-11/18 — PhD in Applied Mathematics en cotutelle: University of Montpellier & Polytechnic University of Milan
PhD thesis: Hybrid High-Order methods for interface problems (TEL tel-01926061 and defense report DR.pdf)
Supervisors: D. A. Di Pietro and L. Formaggia

Research
Preprints
[1] — Gradient discretization of a 3D-2D-1D mixed-dimensional model with resolved interface, application to the drying
of a fractured porous medium
with K. Brenner and R. Masson
Submitted for publication, 2021.
HAL preprint hal-02892526
Journal articles
[4] — A discrete Weber inequality on three-dimensional hybrid spaces with application to the HHO approximation of
magnetostatics
with D. A. Di Pietro and S. Lemaire
Math. Models Methods Appl. Sci., 2021.
HAL preprint hal-02892526, arXiv preprint arXiv:2007.03485
[3] — A Hybrid High-Order method for passive transport in fractured porous media
with D. A. Di Pietro and L. Formaggia
GEM Int. J. Geomath., 2019, 10(12). DOI: 10.1007/s13137-019-0114-x
HAL preprint hal-01784181
[2] — A Hybrid High-Order method for flows in fractured porous media
with D. A. Di Pietro and L. Formaggia
SIAM J. Sci. Comput., 2018, 40(2):A1063–A1094. DOI: 10.1137/17M1119500
HAL preprint hal-01482925, arXiv preprint arXiv:1711.11420
[1] — A Hybrid High-Order method for the Cahn–Hilliard problem in mixed form
with D. A. Di Pietro , F. Marche and F. Pigeonneau
SIAM J. Numer. Anal., 2016, 54(3):1873–1898. DOI: 10.1137/15M1041055
HAL preprint hal-01203733, arXiv preprint arXiv:1509.07384
Conference proceedings
[3] — A three-dimensional Hybrid High-Order method for magnetostatics
with D. A. Di Pietro and S. Lemaire
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples, 2020, p. 255-263.
DOI: 10.1007/978-3-030-43651-3_22, HAL preprint hal-02407175
[2] — Numerical study of the fracture diffusion-dispersion coefficient for passive transport in fractured porous media
Numerical Mathematics and Advanced Applications ENUMATH 2019, 2021, p. 255-263.
DOI: 10.1007/978-3-030-55874-1_24, HAL preprint hal-02412691
[1] — A Hybrid High-Order method for the convective Cahn–Hilliard problem in mixed form
with D. A. Di Pietro and F. Marche
Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems, 2017, p. 517–526.
DOI : 10.1007/978-3-319-57394-6_54, HAL preprint hal-01477247, arXiv preprint arXiv:1702.08224
Theses
[1] — Hybrid High-Order methods for interface problems
PhD thesis, 12 November 2018
Manuscript tel-01926061 and defense report DR.pdf

Presentations
08/2021 — A three-dimensional HHO method for magnetostatics
Italian Society of Applied and Industrial Mathematics, Parma, Italy Online
06/2021 — An hybrid-dimensional model coupling a Darcy flow in fractured porous media and a one dimensional
free flow
SIAM Conference on Mathematical and Computational Issues in the Geosciences, Polytechnic University of Milan, Italy Online
04/2021 — Hybrid High-Order methods and fractured porous media
Web-seminar CEMEF, MINES ParisTech, France.
01/2021 — A three-dimensional HHO method for magnetostatics
European Congress on Computational Methods in Applied Sciences and Engineering, Paris, France Online
11/2020 — Hybrid High-Order methods and application to magnetostatics
Web-seminar ANEDP, Laboratoire Jean Alexandre Dieudonné, Côte d’Azur University, France
06/2020 — A three-dimensional HHO method for magnetostatics
Finite Volumes for Complex Applications 9, Bergen, Norway Online
09/2019 — HHO methods for reduced models in the framework of fractured porous media
European Conference on Numerical Mathematics and Advanced Applications, Egmond aan Zee, The Netherlands
04/2019 — Poster session: HHO methods for reduced models in the framework of fractured porous media
POlytopal Element Methods in Mathematics and Engineering, Marseille (CIRM), France
03/2019 — Hybrid High-Order methods and applications to interface problems
Seminar ANEDP, Laboratoire Paul Painlevé, University of Lille, France
07/2018 — Presentation of a HHO method for flows and passive transport in fractured porous media
Italian Society of Applied and Industrial Mathematics, Rome, Italy
06/2018 — Presentation of a HHO method for flows and passive transport in fractured porous media
International Conference on Boundary and Interior Layers, Glasgow, Scotland
09/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
SIAM Conference on Mathematical and Computational Issues in the Geosciences, Friedrich-Alexander University Erlangen-Nürnberg, Germany
Presentation of a HHO method for Darcy flows in fractured porous media
European Conference on Numerical Mathematics and Advanced Applications, Voss, Norway
08/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
Reliable Methods of Mathematical Modeling 8, Humboldt University of Berlin, Germany
06/2017 — Poster session: A HHO method for the Convective Cahn–Hilliard problem in mixed form
Finite Volumes for Complex Applications 8, University of Lille 1, France
05/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
15th European Finite Element Fair, Polytechnic University of Milan, Italy
01/2017 — Presentation of a HHO method for Darcy flows in fractured porous media
CompGeo - Computational Geosciences @ MOX, Polytechnic University of Milan, Italy
10/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
Numerical Methods for PDEs, Institut Henri Poincare, Paris, France
Poster session: A HHO method for Darcy flows in fractured porous media
GdR MaNu - Mathématiques pour le Nucléaire, St Valery sur Somme, France
06/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece
05/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
14th European Finite Element Fair, University of Bonn, Germany
02/2016 — Presentation of a HHO method and application to the Cahn–Hilliard problem
Seminar ACSIOM, Institut Montpelliérain Alexander Grothendieck, University of Montpellier, France
01/2016 — Calculation of shadows and occlusions in a geometric scene, in collaboration with OPTIS
Semaine d'Etude Maths-Entreprises, Sophia Antipolis, France
10/2015 — Poster session: A HHO method for the Cahn–Hilliard problem in mixed form
POlytopal Element Methods in Mathematics and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
09/2015 — Presentation of the development of a HHO method for the Cahn-Hilliard problem
Saint-Gobain Recherche, Aubervilliers, France

Teaching
2020/21 — Côte d'Azur University
L2 - Numerical Analysis (tutorials)
2019/20 — University of Lille
1st year IMA3 (equiv. L3 at Polytech engineering schools) - Numerical Analysis (lectures, tutorials & TP)
2018/19 — University of Lille
1st year IMA2A3 (equiv. L3 apprenticeship at Polytech engineering schools) - Numerical Analysis (lectures, tutorials & TP)
Extra tutoring/second session - General mathematics (July - August)
2017/18 — University of Montpellier
2nd year PEIP (equiv. L2 at Polytech engineering schools) - Probabilities, Geometry, Topology & Analysis (tutorials)
L1 - Operational research (tutorials)
2016/17 — University of Montpellier
L3 - Numerical analysis of ODEs (TP)
L2 - Introduction to Scientific Software (TP)
L2 - Mathematics for Earth Science (TP)
2015/16 — University of Montpellier
L1 - BioMaths (lectures & tutorials)

Gallery
Meshes
Nonconforming mesh refinement of the 2 dimensional square unit (.typ1 format)
  > mesh5_1  (h = 6.25e-02)
> mesh5_2  (h = 3.12e-02)
> mesh5_3  (h = 1.56e-02)
> mesh5_4  (h = 7.81e-03)
> mesh5_5  (h = 3.91e-03)
> mesh5_6  (h = 1.95e-03)
Numerical experiments
Magnetostatics
3D magnetic field generated by a current flowing through a coil (click to enlarge).
 
Passive transport in fractured porous media
We consider horizontal and "HHO-shaped" fractures that act as barriers (left and center) and vertical fractures that act as conduits (right).
Cahn-Hilliard
We compare three evolutions of the same initial condition, obtained on different Cartesian meshes (128x128, 64x64, 32x32) and different polynomial degrees (0,1,2). The initial condition is a random value between +/- 1 inside each element of the 32x32 Cartesian mesh.
We compare four evolutions of the same initial condition, obtained with different Peclet number. The initial condition is a random value between +/- 1 on each cells that are inside a circular domain of the Voronoi mesh and -1 outside.
We perturb the steady solution in order to show the robustness of the method to capture the interface dynamics subject to a strong circular velocity fields.