41 citations · 111 across the 8 of their papers we have counts for
6 papers · 1 filter
Error estimates of finite difference schemes for the Korteweg-de Vries equation
Clémentine Courtès, Frédéric Lagoutière, Frédéric Rousset
This article deals with the numerical analysis of the Cauchy problem for the Korteweg-de Vries equation with a finite difference scheme. We consider the Rusanov scheme for the hype…
Sharpening methods for finite volume schemes
B Després, S Kokh, Frédéric Lagoutière
We review sharpening methods for finite volume schemes, with an emphasis on the basic structure of sharpening methods. It covers high order methods and non linear techniques for li…
Convergence order of upwind type schemes for transport equations with discontinuous coefficients
François Delarue, Frédéric Lagoutière, Nicolas Vauchelet
An analysis of the error of the upwind scheme for transport equation with discontinuous coefficients is provided. We consider here a velocity field that is bounded and one-sided Li…
Convergence of finite volumes schemes for the coupling between the inviscid Burgers equation and a particle
Nina Aguillon, Frédéric Lagoutière, Nicolas Seguin
In this paper, we prove the convergence of a class of finite volume schemes for the model of coupling between a Burgers fluid and a pointwise particle introduced in [LST08]. In thi…
Convergent and conservative schemes for nonclassical solutions based on kinetic relations
Benjamin Boutin, Christophe Chalons, Frederic Lagoutiere +1
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative a…
Probabilistic analysis of the upwind scheme for transport
Francois Delarue, Frédéric Lagoutière
We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward…