Uniform weak error estimates for an asymptotic preserving scheme applied to a class of slow-fast parabolic semilinear SPDEs

03/20/2022
by   Charles-Edouard Bréhier, et al.
0

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 time scale separation ϵ vanishes, the slow component converges to the solution of a limiting evolution equation, which is captured when the time-step size Δ t vanishes by a limiting scheme. The objective of this work is to prove weak error estimates which are uniform with respect to ϵ, in terms of Δ t: the scheme satisfies a uniform accuracy property. This is a non trivial generalization of a recent article in an infinite dimensional framework. The fast component is discretized using the modified Euler scheme for SPDEs introduced in a recent work. Proving the weak error estimates requires delicate analysis of the regularity properties of solutions of infinite dimensional Kolmogorov equations.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
03/20/2022

Analysis of a modified Euler scheme for parabolic semilinear stochastic PDEs

We propose a modification of the standard linear implicit Euler integrat...
research
07/31/2022

Uniform error bounds for numerical schemes applied to multiscale SDEs in a Wong-Zakai diffusion approximation regime

We study a family of numerical schemes applied to a class of multiscale ...
research
04/29/2021

Asymptotic preserving schemes for SDEs driven by fractional Brownian motion in the averaging regime

We design numerical schemes for a class of slow-fast systems of stochast...
research
10/08/2022

Convergence and error analysis for pure collisional breakage equation

Collisional breakage in the particulate process has a lot of recent curi...
research
08/25/2022

Uniform error estimate of an asymptotic preserving scheme for the Lévy-Fokker-Planck equation

We establish a uniform-in-scaling error estimate for the asymptotic pres...

Please sign up or login with your details

Forgot password? Click here to reset