哈尔滨工业大学（深圳）学术讲座

演讲人Speaker：   梁冬冬  

题目Title: FEM approximation for parabolic optimal control problems with pointwise observations

时间Date：   2023年 7月3日       Time：15:30-16:30

地点Venue： G 栋 514 室

内容摘要Abstract： 

We consider parabolic distributed control problems with cost functional of pointwise observation type either in space or in time. First, we show the well-posedness of the optimization problems and derive the first order optimality systems, where the adjoint state can be expressed as the linear combination of solutions to two backward parabolic equations that involve the Dirac delta distributionas source either in space or in time. Second, we use a space-time finite element method to discretize the control problems, where the state variable is approximated by piecewise constant functions in time and continuous piecewise linear polynomials in space, and the control variable is discretized by following the variational discretization concept. We obtain a priori error estimates for the control and state variables with order up to a logarithmic factor under the L2-norm. Finally, we perform several numerical experiments to support our theoretical results.

个人简介(About the speaker):

    梁冬冬，于2022年6月获四川大学计算数学专业博士学位，导师为谢小平教授，其在博士期间主要研究偏微分方程的有限元方法及偏微分方程最优控制问题的数值理论。现为香港理工大学深圳研究院的在站博士后，合作导师李步扬教授。主要研究方向为偏微分方程的有限元方法、控制问题的数值理论等领域，研究内容包括抛物方程逐点观测的分布最优控制问题、光滑区域上椭圆方程非齐次Dirichlet 边值问题有限元解及其导数的逐点误差估计问题、抛物方程Dirichlet 边界最优控制问题离散解的误差估计等问题，部分结果发表在Numer. Math. Theor. Meth. Appl., Adv. Comput. Math.等刊物上。