Raphael Bulle

Raphael Bulle
Laval University | ULAVAL

Doctor of Engineering
I am working on gradients reconstruction for FEM with applications to error estimation and anisotropic mesh refinement.

About

10
Publications
702
Reads
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7
Citations
Introduction
I am a Post-doctoral researcher at Laval University, Québec in the field of Applied Mathematics. My current work is concerned with the development of new methods of flux recovery with applications to a posteriori error estimation in finite element methods. I am working in collaboration with the French tire company Michelin. I am also interested in the error estimation of nonlocal models and fractional elliptic PDEs discretizations using finite elements.
Additional affiliations
September 2018 - January 2019
University of Luxembourg
Position
  • PhD Student
Description
  • Teaching Mathematik I in Bachelor of Ingénierie - Génie Civil, filière construction (1 semester, 30 Teaching units.)
October 2017 - present
University of Luxembourg
Position
  • PhD Student
Education
September 2013 - July 2014
University of Franche-Comté
Field of study
  • Teaching Mathematics
September 2013 - September 2017
University of Franche-Comté
Field of study
  • Theoretical Mathematics
September 2010 - September 2013
University of Franche-Comté
Field of study
  • Mathematics

Publications

Publications (10)
Thesis
Full-text available
This manuscript is concerned with a posteriori error estimation for the finite element discretization of standard and fractional partial differential equations as well as an application of fractional calculus to the modeling of the human meniscus by poro-elasticity equations. In the introduction, we give an overview of the literature of a posterior...
Preprint
Full-text available
We develop a novel a posteriori error estimator for the L2 error committed by the finite element discretization of the solution of the fractional Laplacian. Our a posteriori error estimator takes advantage of the semi-discretization scheme using a rational approximation which allows to reformulate the fractional problem into a family of non-fractio...
Article
In this study, we observe that the poromechanical parameters in human meniscus vary spatially throughout the tissue. The response is anisotropic and the porosity is functionally graded. To draw these conclusions, we measured the anisotropic permeability and the “aggregate modulus” of the tissue, i.e., the stiffness of the material at equilibrium, a...
Preprint
Full-text available
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank-Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, t...
Poster
Full-text available
In this poster, we present our new hierarchical a posteriori error estimation method for the spectral fractional Laplacian equation with homogeneous Dirichlet boundary condition. The numerical results show the adaptively refined mesh we obtain using our method as well as a convergence comparison where we can notice the sharpness of the estimator an...
Article
We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional te...
Preprint
Full-text available
We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional te...
Article
This work has been initiated during the Maths-Companies study group (Semaine d’Étude Maths-Entreprise, SEME) organised by AMIES (Agence pour les Mathematiques en Interaction avec l’Entreprise et la Société), CNRS (Centre National de la Recherche Scientifique) and the University of Strasbourg from 12th to 18th of November 2018. The subject was propo...

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Projects

Projects (2)
Project
Developing an efficient parallel implementation of fractional PDEs based on a novel a posteriori error estimator and describe its mathematical properties.