Numerical Methods for Parabolic Optimal Control Problem
Prof. Zhi-Yue Zhang
Nanjing Normal University

In this talk, I will present error estimates for solving control problems with parabolic PDEs. In the first part, the immersed finite element method for parabolic optimal control problems with interfaces is proposed. The parabolic state and adjoint state equations are treated with the immersed finite element method. By introducing the auxiliary functions which are the solution of interface parabolic equations with non-homogenous and homogeneous jump conditions, optimal error estimates are proved for the proposed schemes to the control, state and adjoint state in semi-discrete case and fully discrete case. In the second part, based on Galerkin Fourier finite volume element method to discrete the parabolic optimal Dirichlet boundary control on complex connected domains. Both the second order convergence order in space and time for the state, adjoint state and control are obtained. Numerical experiments confirmed the theoretical results for both parts.

About the Speaker

张志跃,南京师范大学数学科学学院教授,博士生导师。2001年毕业于山东大学数学与系统科学学院计算数学专业,获理学博士学位。2002年至2004年曾在中国科学院大气物理研究所从事博士后研究工作。2006年、2007年、2009年和2015年分别赴英国University of Sussex,美国North Carolina State University、University of Washington和North Carolina State University进行学术访问。应邀访问阿曼Sultan Qaboos University数学与统计系,加拿大York University数学与统计系,台湾交通大学数学建模与科学计算中心,静宜大学财务与计算数学系,新加坡National University of Singapore数学科学研究所,韩国Konkuk University和Inha University数学系,在第八届世界华人数学家大会做45分钟报告,发表学术论文六十余篇。目前主要的研究兴趣为偏微分方程数值解、PDE约束的最优控制问题、数值天气预报和计算流体动力学。

2021-03-02 10:00 AM
Room: Tencent Meeting
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