119 citations · 535 across the 49 of their papers we have counts for
29 papers · 1 filter
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…
Certification of PGD reduced-order models with separated spatial variables
Jean Ruel, Ludovic Chamoin, Frédéric Legoll +1
Model order reduction techniques have become an attractive approach for obtaining fast approximations of multidimensional problems. Besides computational efficiency, ensuring the r…
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…
Combining machine-learned and empirical force fields with the parareal algorithm: application to the diffusion of atomistic defects
Olga Gorynina, Frederic Legoll, Tony Lelievre +1
We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [F. Legoll, T…
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…
A pedagogical review on a posteriori error estimation in Finite Element computations
Ludovic Chamoin, Frederic Legoll
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and cla…
An MsFEM approach enriched using Legendre polynomials
Frederic Legoll, Pierre-Loik Rothe, Claude Le Bris +1
We consider a variant of the conventional MsFEM approach with enrichments based on Legendre polynomials, both in the bulk of mesh elements and on their interfaces. A convergence an…
Parareal computation of stochastic differential equations with time-scale separation: a numerical study
Tony Lelièvre, Frédéric Legoll, Keith Myerscough +1
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and…
Goal-oriented error estimation and adaptivity in MsFEM computations
Ludovic Chamoin, Frederic Legoll
We introduce a goal-oriented strategy for multiscale computations performed using the Multiscale Finite Element Method (MsFEM). In a previous work, we have shown how to use, in the…
An embedded corrector problem for homogenization. Part II: Algorithms and discretization
Eric Cancès, Virginie Ehrlacher, Frederic Legoll +2
This contribution is the numerically oriented companion article of the work [E. Cancès, V. Ehrlacher, F. Legoll, B. Stamm and S. Xiang, arxiv preprint 1807.05131]. We focus here on…
An embedded corrector problem for homogenization. Part I: Theory
Eric Cancès, Virginie Ehrlacher, Frederic Legoll +2
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the cont…
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…
A posteriori error estimation and adaptive strategy for the control of MsFEM computations
Ludovic Chamoin, Frederic Legoll
We introduce quantitative and robust tools to control the numerical accuracy in simulations performed using the Multiscale Finite Element Method (MsFEM). First, we propose a guaran…
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…
An embedded corrector problem to approximate the homogenized coefficients of an elliptic equation
Eric Cances, Virginie Ehrlacher, Frederic Legoll +1
We consider a diffusion equation with highly oscillatory coefficients that admits a homogenized limit. As an alternative to standard corrector problems, we introduce here an embedd…
Periodic homogenization using the Lippmann--Schwinger formalism
Sebastien Brisard, Frederic Legoll
When homogenizing elliptic partial differential equations, the so-called corrector problem is pivotal to compute the macroscale effective coefficients from the microscale informati…
A control variate approach based on a defect-type theory for variance reduction in stochastic homogenization
Frederic Legoll, William Minvielle
We consider a variance reduction approach for the stochastic homogenization of divergence form linear elliptic problems. Although the exact homogenized coefficients are determinist…
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…