119 citations · 535 across the 49 of their papers we have counts for
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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…
Pathwise estimates for an effective dynamics
Frederic Legoll, Tony Lelievre, Stefano Olla
Starting from the overdamped Langevin dynamics in , we consider a scalar Markov process which approximate…
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…
An accurate scheme to solve cluster dynamics equations using a Fokker-Planck approach
Thomas Jourdan, Gabriel Stoltz, Frédéric Legoll +1
We present a numerical method to accurately simulate particle size distributions within the formalism of rate equation cluster dynamics. This method is based on a discretization of…