报告题目：Numerical Simulation and Analysis for the Stochastic Navier--Stokes Equations

主 讲 人：赵文举

单 位：山东大学

时 间：6月6日10:00

地 点：学院一楼报告厅

摘 要：

In this talk, we numerically study the stochastic Navier--Stokes equations with a wide range of noises from colored to white in time and space. For each kind of temporal-spatial noises, we present detailed definitions and discussions and their properties. Further we present a Martingale regularization method for the stochastic Navier--Stokes equations with additive noise，where the original system is split into two equivalent parts, the linear stochastic Stokes equations with Martingale solution and the stochastic modified Navier-Stokes equations with relatively-higher regularities. The stability and convergence of numerical scheme for the pathwise modified Navier-Stokes equations are proved. We then apply the discretized colored/white forcings to facilitate numerical experiments in the context of finite element discretizations and compare the efficiency and regularity features of the system resulting from the experiments. The proposed techniques are useful for general stochastic partial differential equations with colored or white forcing.

简 介：

赵文举，山东大学数学学院副研究员，2010年山东师范大学本科毕业，2013年吉林大学硕士，2016年美国佛罗里达州立大学硕士，2016年美国旧金山湾区劳伦斯利弗莫尔国家实验室，2017年美国佛罗里达州立大学博士，2020年南方科技大学数学学院和深圳国际数学中心博士后。研究领域主要包括随机偏微分方程数值解、随机优化控制、计算流体力学和形状优化等。在Numerical Mathematics： Theory， Methods and Applications，SIAM Journal on Scientific Computing，Computer Methods in Applied Mechanics and Engineering，Numerical Methods for Partial Differential Equations，Applied Mathematics Letters等国内外重要学术刊物发表多篇论文。