Charles-Edouard Brehier, Universite Claude Bernard Lyon 1

Chuchu Chen, Associate Professor

Analysis of a modified Euler scheme for parabolic stochastic PDEs

16:00-17:00 April 6(Wednesday)

I will present a new scheme for the weak approximation of solutions of some parabolic semilinear stochastic PDEs driven by space-time white noise, which is a modification of the standard implicit Euler scheme. This new scheme is shown to preserve the spatial regularity of the solution, for any choice of the time-step size. In addition, an approximation result for the invariant distribution in the total variation distance is obtained in the case the nonlinearity is a gradient. Finally, the scheme can be used to design some asymptotic preserving and uniformly accurate schemes for slow-fast systems. 

This talk is based on two recent preprints: 

http://arxiv.org/abs/2203.10598 

http://arxiv.org/abs/2203.10600