65 citations · 149 across the 21 of their papers we have counts for
28 papers
Homogenization of some viscous Hamilton--Jacobi equations using variational arguments on probability spaces
Andrea Braides, Gianni Dal Maso, Claude Le Bris
This work studies the asymptotic behavior of a class of viscous Hamilton--Jacobi equations with oscillatory periodic potentials, already studied by other authors in the PDE framewo…
Numerical homogenization of a linear multiscale conservation law
Claude Le Bris, Frédéric Legoll, Giulia Merlini
We address the numerical approximation of a scalar conservation law with a highly oscillatory flux, in the linear setting. Taking advantage of the intrinsic numerical viscosity of…
A Multiscale Finite Element Method for reaction-diffusion eigenproblems arising from neutronics
Claude Le Bris, Albéric Lefort, Frédéric Legoll
We consider reaction-diffusion eigenproblems with oscillatory diffusion and reaction coefficients. The reaction coefficient magnitude is large: the corrector equation identified by…
MsFEM for advection-dominated problems in heterogeneous media: Stabilization via nonconforming variants
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
We study the numerical approximation of advection-diffusion equations with highly oscillatory coefficients and possibly dominant advection terms by means of the Multiscale Finite E…
Error Estimators for the Small-Biot Lumped Approximation for the Conduction Dunking Problem
Kento Kaneko, Claude Le Bris, Anthony T. Patera
We consider the dunking problem: a solid body at uniform temperature is placed in a environment characterized by farfield temperature and spatially uniform…
Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods
Rutger A. Biezemans, Claude Le Bris, Frédéric Legoll +1
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-…
Non-intrusive implementation of Multiscale Finite Element Methods: an illustrative example
Rutger A. Biezemans, Claude Le Bris, Frederic Legoll +1
Multiscale Finite Element Methods (MsFEM) are finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functi…
Multiscale Finite Element methods for advection-dominated problems in perforated domains
Claude Le Bris, Frederic Legoll, Francois Madiot
We consider an advection-diffusion equation that is advection-dominated and posed on a perforated domain. On the boundary of the perforations, we set either homogeneous Dirichlet o…
Fourier-based numerical approximation of the Weertman equation for moving dislocations
Marc Josien, Yves-Patrick Pellegrini, Frédéric Legoll +1
This work discusses the numerical approximation of a nonlinear reaction-advection-diffusion equation, which is a dimensionless form of the Weertman equation. This equation models s…
Perturbation problems in homogenization of hamilton-jacobi equations
Pierre Cardaliaguet, Claude Le Bris, Panagiotis Souganidis
This paper is concerned with the behavior of the ergodic constant associated with convex and superlinear Hamilton-Jacobi equation in a periodic environment which is perturbed eithe…
On the best constant matrix approximating an oscillatory matrix-valued coefficient in divergence-form operators
Claude Le Bris, Frederic Legoll, Simon Lemaire
We approximate an elliptic problem with oscillatory coefficients using a problem of the same type, but with constant coefficients. We deliberately take an engineering perspective,…
Stable approximation of the advection-diffusion equation using the invariant measure
Claude Le Bris, Frederic Legoll, Francois Madiot
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the…
Examples of computational approaches to accommodate randomness in elliptic PDEs
Claude Le Bris, Frederic Legoll
We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manip…
A numerical comparison of some Multiscale Finite Element approaches for convection-dominated problems in heterogeneous media
Claude Le Bris, Frederic Legoll, François Madiot
The purpose of this work is to investigate the behavior of Multiscale Finite Element type methods for advection-diffusion problems in the advection-dominated regime. We present, st…
Some variance reduction methods for numerical stochastic homogenization
Xavier Blanc, Claude Le Bris, Frederic Legoll
We overview a series of recent works devoted to variance reduction techniques for numerical stochastic homogenization. Numerical homogenization requires solving a set of problems a…
Special Quasirandom Structures: a selection approach for stochastic homogenization
Claude Le Bris, Frederic Legoll, William Minvielle
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state…
Adaptive low-rank approximation and denoised Monte-Carlo approach for high-dimensional Lindblad equations
Claude Le Bris, Pierre Rouchon, Julien Roussel
We present a twofold contribution to the numerical simulation of Lindblad equations. First, an adaptive numerical approach to approximate Lindblad equations using low-rank dynamics…
Macroscopic limit of a one-dimensional model for aging fluids
David Benoit, Claude Le Bris, Tony Lelièvre
We study a one-dimensional equation arising in the multiscale modeling of some non-Newtonian fluids. At a given shear rate, the equation provides the instantaneous mesoscopic respo…
An MsFEM type approach for perforated domains
Claude Le Bris, Frederic Legoll, Alexei Lozinski
We follow up on our previous work [C. Le Bris, F. Legoll and A. Lozinski, Chinese Annals of Mathematics 2013] where we have studied a multiscale finite element (MsFEM) type method…
Mathematical analysis of a one-dimensional model for an aging fluid
David Benoit, Lingbing He, Claude Le Bris +1
We study mathematically a system of partial differential equations arising in the modelling of an aging fluid, a particular class of non Newtonian fluids. We prove well-posedness o…
Multiscale Finite Element approach for "weakly" random problems and related issues
C. Le Bris, F. Legoll, F. Thomines
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the pertur…
Rate of convergence of a two-scale expansion for some "weakly" stochastic homogenization problems
C. Le Bris, F. Legoll, F. Thomines
We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation…
Symmetric parareal algorithms for Hamiltonian systems
X. Dai, C. Le Bris, F. Legoll +1
The parareal in time algorithm allows to efficiently use parallel computing for the simulation of time-dependent problems. It is based on a decomposition of the time interval into…
Symplectic schemes for highly oscillatory Hamiltonian systems: the homogenization approach beyond the constant frequency case
Matthew Dobson, Claude Le Bris, Frederic Legoll
We follow up on our previous works which presented a possible approach for deriving symplectic schemes for a certain class of highly oscillatory Hamiltonian systems. The approach c…