41 citations · 111 across the 8 of their papers we have counts for
12 papers
Two-phase averaged system justification for ideal gases without conductivity
D Bresch, C Burtea, P Gonin--Joubert +1
This article concerns the mathematical justification of an averaged system of partial differential equations governing the evolution of a two-phase mixture of compressible ideal fl…
Relaxation limit of the aggregation equation with pointy potential
Benoît Fabrèges, Frédéric Lagoutière, Tran Tien +1
This work is devoted to the study of a relaxation limit of the so-called aggregation equation with a pointy potential in one dimensional space. The aggregation equation is by now w…
Physical Relaxation Terms for Compressible Two-Phase Systems
Didier Bresch, Cosmin Burtea, Frédéric Lagoutière
In this note, we propose the first mathematical derivation of a macroscopic Baer-Nunziato type system for compressible two-phase flows allowing two pressure state laws depending on…
The Neumann numerical boundary condition for transport equations
Jean-François Coulombel, Frédéric Lagoutière
In this article, we show that prescribing homogeneous Neumann type numerical boundary conditions at an outflow boundary yields a convergent discretization in for tran…
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…
Convergence analysis of upwind type schemes for the aggregation equation with pointy potential
François Delarue, Frédéric Lagoutìère, Nicolas Vauchelet
A numerical analysis of upwind type schemes for the nonlinear nonlocal aggregation equation is provided. In this approach, the aggregation equation is interpreted as a conservative…
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…
The Filippov characteristic flow for the aggregation equation with mildly singular potentials
José Antonio Carrillo, Francois James, Frédéric Lagoutière +1
Existence and uniqueness of global in time measure solution for the multidimensional aggregation equation is analyzed. Such a system can be written as a continuity equation with a…
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…