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

凤小兵 教授(田纳西大学)
Wednesday, July 1st, 2020, 8:00 PM  腾讯会议 ID:590 950 658
主持人:朱升峰 副教授
报告平台:腾讯会议 ID:590 950 658

报告人介绍:美国田纳西大学数学终身教授,曾任数学系副系主任,数学系研究生学部主任。1983 年和1985 年分别获西安交大计算数学学士和硕士学位,1992年获美国普度大学(Purdue University)应用和计算数学博士学位。凤小兵教授长期从事线性,特别是非线性确定和随机偏微分方程及其数值解法与算法的研究,并取得了一系列国际领先的成果。在SIAM Review, SIAM J. Numerical Analysis, Mathematics of Computation, Numerische Mathematik, SIAM J. Mathematical Analysis, Transaction of AMS, Calculus of Variation and PDEs等国际一流专业学术期刊上发表论100余篇。

报告内容摘要: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 have very low regularity in time (and in space), which then poses a significant challenge for developing efficient and convergent numerical methods for the stochastic Stokes and Navier-Stokes equations. In particular, the most natural and popular class of numerical methods for those equations, namely mixed finite element methods, had not been proven to work. In this talk I shall present some recent developments in mixed finite element methods for the Stokes and Navier-Stokes equations with multiplicative noise. I shall highlight the establishment of the continuous and discrete stochastic inf-sup conditions and the strong convergence not only for the velocity approximation but also for the pressure approximation, as well as the new analysis techniques used to obtain these results. Numerical experiments will also be presented to validate the theoretical results.
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