250 citations · 1.1k across the 130 of their papers we have counts for
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Asymptotic structure of cosmological fluid flows in one and two space dimensions: a numerical study
Yangyang Cao, Mohammad A. Ghazizadeh, Philippe G. LeFloch
We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing suc…
Augmented hyperbolic models with diffusive-dispersive shocks
Philippe G. LeFloch, Allen M. Tesdall
Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock w…
Mesh-free error integration in arbitrary dimensions: a numerical study of discrepancy functions
Philippe G. LeFloch, Jean-Marc Mercier
We are interested in mesh-free formulas based on the Monte-Carlo methodology for the approximation of multi-dimensional integrals, and we investigate their accuracy when the functi…
Asymptotic structure of cosmological Burgers flows in one and two space dimensions: a numerical study
Yangyang Cao, Mohammad A. Ghazizadeh, Philippe G. LeFloch
We study the cosmological Burgers model, as we call it, which is a nonlinear hyperbolic balance law (in one and two spatial variables) posed on an expanding or contracting backgrou…
The Transport-based Mesh-free Method (TMM) and its applications in finance: a review
Philippe G. LeFloch, Jean-Marc Mercier
We review a numerical technique, referred to as the Transport-based Mesh-free Method (TMM), and we discuss its applications to mathematical finance. We recently introduced this met…
The seed-to-solution method for the Einstein constraints and the asymptotic localization problem
Philippe G. LeFloch, The-Cang Nguyen
We establish the existence of a class of asymptotically Euclidean solutions to Einstein's constraint equations, whose asymptotic behavior at infinity is arbitrarily prescribed. The…