3 papers
math.AP2024
Nonlinear orbital stability of stationary discrete shock profiles for scalar conservation laws
Lucas Coeuret
For scalar conservation laws, we prove that spectrally stable stationary Lax discrete shock profiles are nonlinearly stable in some polynomially-weighted and …
math.NA2023
Linear stability of discrete shock profiles for systems of conservation laws
Lucas Coeuret
We prove the linear orbital stability of spectrally stable stationary discrete shock profiles for conservative finite difference schemes applied to systems of conservation laws. Th…
math.NA2023
Tamed stability of finite difference schemes for the transport equation on the half-line
Lucas Coeuret
In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numer…