报告人：李步扬（香港理工大学）
报告题目: Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint
报告摘要：In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The fully discrete scheme is obtained by applying the conforming linear Galerkin finite element method in space, with L1 scheme or backward Euler convolution quadrature in time, and the control variable by a variational type discretization. With a space mesh size $h$ and time stepsize $\tau$, we prove the following order of convergence for the numerical solutions of the optimal control problem: $O(\tau^{\min({1}/{2}+\alpha-\epsilon,1)}+h^2)$ in the discrete $L^2(0,T;L^2(\Omega))$ norm and $O(\tau^{\alpha-\epsilon}+\ell_h^2h^2)$ in the discrete $L^\infty(0,T;L^2(\Omega))$ norm, with an arbitrarily small positive number $\epsilon$ and a logarithmic factor $\ell_h=\ln(2+1/h)$. Numerical experiments are provided to support the theoretical results.
报告人简介：李步扬，2012年于香港城市大学获得博士学位，2015-2016年为德国University of Tuebingen洪堡学者。目前就职于香港理工大学。主要研究方向为微分方程数值解。主要工作发表在《SIAM J. Numer. Anal.》《Numer. Math.》《Math. Comput.》《J. Comput. Phys.》等著名计算数学SCI杂志上，目前已发表论文近40篇。
报告时间：2017年11月4日(星期六)下午16：30-18：00
报告地点: 科技楼南楼702室
