應yl7703永利官網(wǎng)鄧偉華教授的邀請，香港理工大學應用數(shù)學系助理教授李步揚博士將于近期訪問我校，期間將做學術(shù)報告。
      題  目 (一)：Runge-Kutta time discretization of nonlinear parabolic equations studied via discrete maximal parabolic regularity
      時         間：2018年1月15日9:00
      地         點：齊云樓911室
      報 告 摘 要：For a large class of fully nonlinear parabolic equations, which include gradient flows for energy functionals that depend on the solution gradient, the semidiscretization in time by implicit Runge–Kutta methods such as the Radau IIA methods of arbitrary order is studied. Error bounds are obtained in the $W^{1,\infty}$ norm uniformly on bounded time intervals and, with an improved approximation order, in the parabolic
energy norm. The proofs rely on discrete maximal parabolic regularity.
      This is used to obtain $W^{1,\infty}$ estimates, which are the key to the numerical analysis of these problems.

      題  目 (二)：Pointwise-in-time error estimates for an optimal control problem with subdiffusion constraint
      時         間：2018年1月16日9:00
      地         點：齊云樓911室
      報 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: $O(\tau^{\min(1/2+\alpha-\varepsilon,1)}+h^2)$ in the discrete  $L^2(0,T;L^2(\Omega))$ norm and $O(\tau^{\alpha-\varepsilon}+l_{h}^2h^2)$ in the discrete $L^{\infty}(0,T;L^2(\Omega))$ norm, with an arbitrarily small positive number $\varepsilon$ and a logarithmic factor $l_h=\ln(2+1/h)$. Numerical experiments are provided to support the theoretical results.

      歡迎廣大師生光臨！

個人簡介
      李步揚博士于2005年在山東大學取得數(shù)學學士學位，并分別于2007、2009 及2012年在香港城市大學取得應用數(shù)學碩士、哲學碩士及博士學位。李博士于2012年12月開始任職于南京大學，并于2015年7月晉升為副教授。在2015年 6月至2016年5月期間，李博士在德國圖賓根大學兼任洪堡學者的工作。李博士2016年6月加入香港理工大學應用數(shù)學系擔任助理教授一職。李博士當前的主要研究方向是偏微分方程的數(shù)值解法和數(shù)值分析，在SIAM J. Numer. Anal., SIAM J. Sci. Comput., Math. Comput., Numer. Math.  等計算數(shù)學頂級期刊上發(fā)表論文40多篇。

應用數(shù)學與復雜系統(tǒng)省級重點實驗室
                                         yl7703永利官網(wǎng)
                                            萃英學院
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