André Harnist

André Harnist
Inria of Paris

Post-doctoral researcher

About

9
Publications
518
Reads
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27
Citations
Additional affiliations
October 2018 - present
Université de Montpellier
Position
  • PhD Student
Description
  • The goal of this PhD thesis is to develop, analyze, and implement novel Hybrid High-Order (HHO) discretizations of complex problems in fluid mechanics. 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.
Education
September 2016 - September 2018
Université de Montpellier
Field of study
  • Mathematics, Modelization and numerical analysis of PDEs
September 2013 - September 2016
La Rochelle Université
Field of study
  • Mathematics

Publications

Publications (9)
Article
In this work, we design and analyse a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection laws, which are associated with possibly different Sobolev exponents $r\in (1,\infty )$ and $s\in (1,\infty )$. A...
Thesis
Full-text available
The work of this thesis focuses on the development and analysis of Hybrid High-Order (HHO) discretization methods for complex problems in fluid mechanics. HHO methods are a new class of PDEs discretization methods, capable of handling general polytopic meshes. We are interested in problems involving non-Newtonian fluids, more precisely in a non-Hil...
Thesis
Les travaux de cette thèse portent sur le développement et l'analyse de méthodes de discrétisation Hybrides d'Ordre Élevé (HHO: Hybrid High-Order, en anglais) pour des problèmes complexes en mécanique des fluides. Les méthodes HHO sont une nouvelle classe de méthodes de discrétisation des EDPs, capable de gérer des maillages polytopiques généraux....
Article
Full-text available
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of conver...
Presentation
Full-text available
We design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed discretization hinges on discontinuous polynomial unknowns on the mesh and on its skeleton, from which discrete differential operators are reconstructed. The reco...
Preprint
Full-text available
In this work, we design and analyze a Hybrid High-Order (HHO) discretization method for incompressible flows of non-Newtonian fluids with power-like convective behaviour. We work under general assumptions on the viscosity and convection laws, that are associated with possibly different Sobolev exponents r > 1 and s > 1. After providing a novel weak...
Article
Full-text available
We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray–Lions problems set in \(W^{1,p}\) with \(p\in (1,2]\). Specifically, we prove that, depending on the degeneracy of the problem, the convergence rate may vary between \((k+1)(p-1)\) and \((k+1)\), with k denoting the degree of the HHO approximation. These regime-dep...
Preprint
Full-text available
We derive novel error estimates for Hybrid High-Order (HHO) discretizations of Leray-Lions problems set in W^(1,p) with p ∈ (1, 2]. Specifically, we prove that, depending on the degeneracy of the problem, the convergence rate may vary between (k + 1)(p − 1) and (k + 1), with k denoting the degree of the HHO approximation. These regime-dependent err...
Preprint
Full-text available
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of conver...

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