Xiaobing Feng, Professor, University of Tennessee, USA

Pingbing Ming, Professor

Recent developments in numerical methods for stochastic Stokes and Navier-Stokes equations

9:00-10:00 November 11(Friday), Tencent Meeting ID: 898-548-539

Besides the mathematical interests, stochastic Stokes and Navier-Stokes equations have been proposed to study turbulence flow under random forcing. Even in the simplest setting, their PDE solutions are quite rough, which then poses a significant challenge for developing convergent and efficient numerical methods for them.  In particular,  numerical experiments have shown that the well-known and popular numerical methods (such as mixed finite element methods, projection methods, stabilized methods) for their deterministic counterparts do not work well in the stochastic setting.  In this talk I shall first present some recent progress in understanding the underlying mechanisms that contribute to the underperformance of those popular numerical methods for the stochastic Stokes and Navier-Stokes  equations. I shall then discuss some proposed remedies for improving and saving those numerical methods so that they can perform optimally in the stochastic setting and give a brief summary of some other latest developments.