55 citations · 139 across the 23 of their papers we have counts for
16 papers · 1 filter
Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation
Charles-Edouard Bréhier, Jianbo Cui, Xiaojie Wang
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise.…
Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs
Charles-Edouard Bréhier
We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the…
Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs
Charles-Edouard Bréhier
We propose a modification of the standard linear implicit Euler integrator for the weak approximation of parabolic semilinear stochastic PDEs driven by additive space-time white no…
Splitting integrators for stochastic Lie--Poisson systems
Charles-Edouard Bréhier, David Cohen, Tobias Jahnke
We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisso…
Convergence analysis of explicit stabilized integrators for parabolic semilinear stochastic PDEs
Assyr Abdulle, Charles-Edouard Bréhier, Gilles Vilmart
Explicit stabilized integrators are an efficient alternative to implicit or semi-implicit methods to avoid the severe timestep restriction faced by standard explicit integrators ap…
On Asymptotic Preserving schemes for a class of Stochastic Differential Equations in averaging and diffusion approximation regimes
Charles-Edouard Bréhier, Shmuel Rakotonirina-Ricquebourg
We introduce and study a notion of Asymptotic Preserving schemes, related to convergence in distribution, for a class of slow-fast Stochastic Differential Equations. In some exampl…
Strong rates of convergence of a splitting scheme for Schrödinger equations with nonlocal interaction cubic nonlinearity and white noise dispersion
Charles-Edouard Bréhier, David Cohen
We analyse a splitting integrator for the time discretization of the Schrödinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that thi…
Approximation of the invariant distribution for a class of ergodic SDEs with one-sided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme
Charles-Edouard Bréhier
We consider the long-time behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a one-sided Lipschitz c…
Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme
Charles-Edouard Bréhier
We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by addi…
Analysis of a splitting scheme for a class of nonlinear stochastic Schrödinger equations
Charles-Edouard Bréhier, David Cohen
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrödinger equations driven by additive Itô noise. The…
On parareal algorithms for semilinear parabolic Stochastic PDEs
Charles-Edouard Bréhier, Xu Wang
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes,…
Weak convergence rates of splitting schemes for the stochastic Allen-Cahn equation
Charles-Edouard Bréhier, Ludovic Goudenège
This article is devoted to the analysis of the weak rates of convergence of schemes introduced by the authors in a recent work, for the temporal discretization of the stochastic Al…
Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
Charles-Edouard Bréhier, Ludovic Goudenège
We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting…
Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme
Charles-Edouard Bréhier, Marie Kopec
We study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure . We show that the…
Analysis of the Monte-Carlo error in a hybrid semi-lagrangian scheme
Charles-Edouard Bréhier, Erwan Faou
We consider Monte-Carlo discretizations of partial differential equations based on a combination of semi-lagrangian schemes and probabilistic representations of the solutions. We s…
Strong and weak order in averaging for SPDEs
Charles-Edouard Bréhier
We show an averaging result for a system of stochastic evolution equations of parabolic type with slow and fast time scales. We derive explicit bounds for the approximation error w…