报告时间：2024年11月29日（星期五）16:00-17:00

报告地点：翡翠湖校区科教楼B1710室

报 告 人：乔中华 教授

工作单位：香港理工大学

举办单位：数学学院

报告简介：

The global-in-time energy estimate is derived for the second-order accurate exponential time differencing Runge--Kutta (ETDRK2) numerical scheme to the phase field crystal (PFC) equation, a sixth-order parabolic equation modeling crystal evolution. To recover the value of stabilization constant, some local-in-time convergence analysis has been reported, and the energy stability becomes available over a fixed final time. In this work, we develop a global-in-time energy estimate for the ETDRK2 numerical scheme to the PFC equation by showing the energy dissipation property for any final time. An a priori assumption at the previous time step, combined with a single-step $H^2$ estimate of the numerical solution, is the key point in the analysis. Such an $H^2$ estimate recovers the maximum norm bound of the numerical solution at the next time step, and then the value of the stabilization parameter can be theoretically justified. This justification ensures the energy dissipation at the next time step, so that the mathematical induction can be effectively applied, by then the global-in-time energy estimate is accomplished. This paper represents the first effort to theoretically establish a global-in-time energy stability analysis for a second-order stabilized numerical scheme in terms of the original free energy functional. The presented methodology is expected to be available for many other Runge--Kutta numerical schemes to the gradient flow equations.

报告人简介：

乔中华博士于2006年在香港浸会大学获得博士学位，现为香港理工大学应用数学系教授，中科院数学与系统科学研究院——香港理工大学应用数学联合实验室港方副主任，中国工业与应用数学学会理事，中国数学会计算数学分会副理事长。

乔博士主要从事数值微分方程方面算法设计及分析，近年来研究工作集中在相场方程的数值模拟及计算流体力学的高效算法。他至今在SCI期刊上发表论文80余篇，文章被合计引用3000余次。他于2013年获香港研究资助局颁发2013至2014年度杰出青年学者奖，于2018年获得香港数学会青年学者奖，并且于2020年获得香港研究资助局研究学者奖。