*主持人：朱升峰 副教授
*时间：2020年12月11日13:00-14:00
*地点：闵行校区数学楼102报告厅

*讲座内容简介：
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the L^2 norm and an energy space seminorm. We prove well-posedness and regularity results for both problems, develop finite element discretizations for both problems, and prove finite element error estimates for the latter problem. The motivation to study the energy space problem follows from our analysis: we prove that the choice of the control space L2(\Omega) can lead to an optimal control with discontinuities at the corners, even when the domain is convex. We observe this phenomenon in numerical experiments. This behavior does not occur in Dirichlet boundary control problems for the Poisson equation on convex polygonal domains, and may not be desirable in real applications. For the energy space problem, we derive the first order optimality conditions, and show that the solution of the control problem is more regular than the solution of the problem with the L2(\Omega) regularization. We also prove a priori error estimates for the control in the energy norm, and present several numerical experiments for both control problems on convex and nonconvex domains.

*主讲人简介：
龚伟，中国科学院数学与系统科学研究院副研究员，博士生导师，2009年获中国科学院数学与系统科学研究院理学博士学位，2010年获德国洪堡基金会资助赴德国汉堡大学做博士后研究，2017年受“陈景润未来之星”特优人才计划资助。在偏微分方程约束优化及最优控制问题的数学理论及数值算法等方面取得一系列重要成果。承担及参与国家重点研发计划项目、973计划项目及国家自然科学基金等多个项目。