90 citations · 370 across the 42 of their papers we have counts for
6 papers · 1 filter
Analysis of exponential splitting methods for inhomogeneous parabolic equations
Erwan Faou, Alexander Ostermann, Katharina Schratz
We analyze the convergence of the exponential Lie and exponential Strang splitting applied to inhomogeneous second-order parabolic equations with Dirichlet boundary conditions. A r…
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
Erwan Faou, Katharina Schratz
We consider the Klein-Gordon equation in the non-relativistic limit regime, i.e. the speed of light c tending to infinity. We construct an asymptotic expansion for the solution wit…
Fast weak-KAM integrators for separable Hamiltonian systems
Anne Bouillard, Erwan Faou, Maxime Zavidovique
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to…
Sparse spectral approximations for computing polynomial functionals
Erwan Faou, Fabio Nobile, Christophe Vuillot
We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are…
Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
Dario Bambusi, Erwan Faou, Benoit Grebert
In this paper we study the long time behavior of a discrete approximation in time and space of the cubic nonlinear Schrödinger equation on the real line. More precisely, we conside…
Quasi-periodic solutions of the 2D Euler equation
Nicolas Crouseilles, Erwan Faou
We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles…