André Harnist

IMAG Laboratory - University of Montpellier

About

Name André Harnist
Roles PhD student in 3rd year
Representative of the Mathematic and Biostatistic PhD students
Affiliation University of Montpellier, IMAG Laboratory, ACSIOM team
Curriculum vitæ CV [PDF]

Contact

Email andre.harnist@umontpellier.fr
Address Case courrier 051, Place Eugène Bataillon, 34095 Montpellier CEDEX 5, France
Office n°115, 1st floor, Building 9 [Map]
Social network Researchgate Linkedin Google Orcid
André HARNIST

The PhD

Title Hybrid High-Order method for complex problems in fluid mechanics
Field Mathematics
Branches EDP analysis, Numerical analysis, Fluid mechanics
Key words Hybrid High-Order methods, Leray-Lions, Navier-Stokes,
Non-Newtonian fluids, Error estimate, Convergence by compactness
Director Daniele A. Di Pietro
Graduate school i2S (Information Structures Systèmes)
Dates Oct 1, 2018 - Oct 1, 2021 (3 years)

Research

Publications

Dec 9, 2020 Preprint [PDF]
Daniele A. Di Pietro, Jérôme Droniou, and André Harnist (CA)
Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems
HAL preprint hal-03049154
arXiv preprint arXiv:2012.05122
Mar 25, 2020 Preprint [PDF]
Michele Botti, Daniel Castanon Quiroz, Daniele A. Di Pietro, and André Harnist (CA)
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
HAL preprint hal-02519233
arXiv preprint arXiv:2003.13467.

Presentations

Jan 31, 2021 Online talk [PDF]
Improved error estimates for Hybrid High-Order discretizations of Leray-Lions problems
ANZIAM Annual Conference 2021, Virtual event, Australia
Jan 11, 2021 Online talk [PDF]
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
Eccomas Congress 2020 & 14th WCCM, Virtual event, France
Sep 14, 2020 Online talk
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
Conference on Scientific Computing Algoritmy 2020 at Vysoke Tatry, Podbanske, Slovakia
Feb 12, 2020 Talk
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
PhD students day at IMAG, Montpellier, France
Jul 4, 2019 Poster [PDF]
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
Doctiss 2019 day at i2S, Montpellier, France
First prize for the best poster!
Apr 29, 2019 Poster
A Hybrid High-Order method for creeping flows of non-Newtonian fluids
POEMS 2019 conference at CIRM, France

Teaching

2020-2021 Mathematics of decision - 3rd year degree
Person in charge: Lecture, Tutorial, Practical work (64h)
Groups 1 and 2 of cursus IG3 at Polytech Montpellier
Resources:
Lectures: CM1, CM2
Tutorials: TD1, TD2
Practical works: TP1, TP2
2019-2020
2018-2019

Studies

2018 - 2021 PhD in Mathematics
Hybrid High-Order method for complex problems in fluid mechanics
Supervised by Daniele A. Di Pietro, ACSIOM team, IMAG laboratory, Montpellier, France
Subject summary
Hybrid High-Order methods are a recent and highly innovative class of new generation numerical methods for PDEs that aim at overcoming the limitations of traditional discretization methods such as Finite Element or Finite Volumes. Their most prominent features include:
  • support of general polytopal meshes in arbitrary space dimension,
  • arbitrary approximation order,
  • compliance with the physics,
  • reduced computational cost thanks to hybridization, static condensation, and compact stencil.
The goal of this PhD thesis is to develop, analyze, and implement novel HHO discretizations of complex problems in fluid mechanics. We specifically aim at treating generalized Newtonian fluids where the shear stress function exhibits a nonlinear dependency on the shear rate, and possibly include the challenging variable density case. The convergence analysis will rely on both standard error estimates and compactness arguments. This will require to develop discrete functional analysis lemmas whose interest will go beyond applications to computational fluid mechanics. The implementation will rely on the spafedte library, and will benefit from the latest advances in C++ programming.
Formation list (174h) Teaching
  • MOOC Training to teach in higher education
  • How to have an innovative pedagogy? (Sylvain Rouanet)
  • Why and how to develop interactive courses? (Sylvain Rouanet)
  • Introduction to teaching tools for higher education (Sébastien Balme)
  • Prepare, organize and conduct a course (Nathalie Berda)
  • Public speaking (Marc Dumas)
Research and integration
  • Eccomas Congress 2020 & 14th WCCM, Virtual event
  • XXIièmes Louis Antoine Numerical Analysis day at Rennes (Robert Eymard, Francis Filbet)
  • MOOC Research integrity in scientific professions
Miscellaneous
  • Level 1 Prevention and Civic Assistance training
2018 1st in the i2S doctoral competition in Mathematics at IMAG, Montpellier, France
2016 - 2018 Master's degree in Mathematics
MANU (Modelization and numerical analysis of PDEs), University of Montpellier, France
with distinction « Très Bien »
Course list
Internship (6 months) : Hybrid-High Order method for creeping flows of power-law fluids
Supervised by Daniele A. Di Pietro, ACSIOM team, IMAG laboratory, Montpellier, France
2013 - 2016 Bachelor's degree in Mathematics
Research option
University of La Rochelle, France
with distinction « Bien »
Internship (5 weeks) : Modelization of the growth of tree leaves by the algorithm of Qinglan Xia
Supervised by Michel Berthier and Catherine Choquet, MIA laboratory, La Rochelle, France
2013 Baccalaureate
STL (Sciences et Technologies de Laboratoire) option
Lycée de la Venise Verte, Niort, France
with distinction « Assez Bien »

Other

The American Mathematical Monthly

The American Mathematical Monthly is a journal in which university researchers post problems and challenge the readers to solve them. I am citing here some problems that I solved during my studies before starting my thesis which turned out to be challenging enough.

Apr 2018 Problem 11933 [PDF] - with Megan Cook
Problem 11932 [PDF]
Gerald A. Edgar, Daniel H. Ullman & Douglas B. West (2018)
Problems and Solutions, The American Mathematical Monthly, 125:5, 466-475
DOI: 10.1080/00029890.2018.1447207
Sep 2016 Problem 11918 [PDF]
Gerald A. Edgar, Daniel H. Ullman & Douglas B. West (2018)
Problems and Solutions, The American Mathematical Monthly, 125:3, 276-283
DOI: 10.1080/00029890.2018.1424478
Mar 2016 Problem 11884 [PDF] - with Megan Cook
Gerald A. Edgar, Daniel H. Ullman & Douglas B. West (2017)
(2017) Problems and Solutions, The American Mathematical Monthly, 124:10, 970-978
DOI: 10.4169/amer.math.monthly.124.10.970