4 citations · 10 across the 11 of their papers we have counts for
12 papers
Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion
Charles-Edouard Bréhier, David Cohen, Gijs Custers
We consider a class of SPDEs driven by a standard real-valued Brownian motion, with drift and diffusion coefficients such that there exists a unique mild solution taking values in…
Explicit domain preserving numerical schemes for a class of stochastic differential equations
Charles-Edouard Bréhier, David Cohen
We construct and analyze numerical schemes for systems of stochastic differential equations, which preserve almost surely a given hypercube of arbitrary dimension. We propose a new…
Analysis of a first-order explicit positivity preserving scheme for a class of scalar SDEs
Charles-Edouard Bréhier, David Cohen
We propose and analyze a first-order numerical scheme for a class of scalar Itô stochastic differential equations with almost surely positive solutions. We construct a new explicit…
General non-linear fragmentation with discontinuous Galerkin methods
Maxime Lombart, Charles-Edouard Bréhier, Mark Hutchison +1
Dust grains play a significant role in several astrophysical processes, including gas/dust dynamics, chemical reactions, and radiative transfer. Replenishment of small-grain popula…
Numerical simulations of a stochastic dynamics leading to cascades and loss of regularity: applications to fluid turbulence and generation of fractional Gaussian fields
Geoffrey Beck, Charles-Edouard Bréhier, Laurent Chevillard +2
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has bee…
Splitting integrators for linear Vlasov equations with stochastic perturbations
Charles-Edouard Bréhier, David Cohen
We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative…
Numerical approximation of the invariant distribution for a class of stochastic damped wave equations
Ziyi Lei, Charles-Edouard Bréhier, Siqing Gan
We study a class of stochastic semilinear damped wave equations driven by additive Wiener noise. Owing to the damping term, under appropriate conditions on the nonlinearity, the so…
Positivity-preserving schemes for some nonlinear stochastic PDEs
Charles-Edouard Bréhier, David Cohen, Johan Ulander
We introduce a positivity-preserving numerical scheme for a class of nonlinear stochastic heat equations driven by a purely time-dependent Brownian motion. The construction is insp…
Analysis of a positivity-preserving splitting scheme for some nonlinear stochastic heat equations
Charles-Edouard Bréhier, David Cohen, Johan Ulander
We construct a positivity-preserving Lie--Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of nonlinear stochastic…
Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime
Charles-Edouard Bréhier
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-know…
Uniform strong and weak error estimates for numerical schemes applied to multiscale SDEs in a Smoluchowski-Kramers diffusion approximation regime
Charles-Edouard Bréhier
We study a family of numerical schemes applied to a class of multiscale systems of stochastic differential equations. When the time scale separation parameter vanishes, a well-know…
Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations
Charles-Edouard Bréhier, David Cohen, Giuseppe Giordano
We design and study splitting integrators for the temporal discretization of the stochastic FitzHugh--Nagumo system. This system is a model for signal propagation in nerve cells wh…