86 citations · 163 across the 22 of their papers we have counts for
14 papers · 1 filter
Nonlinear orbital stability of stationary shock profiles for the Lax-Wendroff scheme
Jean-François Coulombel, Grégory Faye
In this article we study the spectral, linear and nonlinear stability of stationary shock profile solutions to the Lax-Wendroff scheme for hyperbolic conservation laws. We first cl…
Sharp stability for finite difference approximations of hyperbolic equations with boundary conditions
Jean-François Coulombel, Grégory Faye
In this article, we consider a class of finite rank perturbations of Toeplitz operators that have simple eigenvalues on the unit circle. Under a suitable assumption on the behavior…
Discrete transparent boundary conditions for the two-dimensional leap-frog scheme
Christophe Besse, Jean-François Coulombel, Pascal Noble
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equ…
On the Mach stem configuration with shallow angle
Jean-François Coulombel, Mark Williams
The aim of this article is to explain why similar weak stability criteria appear in both the construction of steady Mach stem configurations bifurcating from a reference planar sho…
Weakly nonlinear surface waves in magnetohydrodynamics
Olivier Pierre, Jean-François Coulombel
This work is devoted to the construction of weakly nonlinear, highly oscillating, current vortex sheet solutions to the incompressible magnetohydrodynamics equations. Current vorte…
Geometric optics for surface waves in nonlinear elasticity
Jean-Francois Coulombel, Mark Williams
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. We consider surface waves (or more precisely, Rayleigh wa…