报告人：Cheng Wang 教授 麻省大学达特茅斯分校
报告时间：2024年7月9日16:00-17:00
报告地点：红瓦楼826
报告内容简介：The global in time energy estimate is derived for the ETDRK2 numerical scheme for the phase field crystal (PFC) equation, a sixth order parabolic equation to model crystal evolution. The energy stability is available for the exponential time differencing Runge-Kutta (ETDRK) numerical scheme to the gradient flow equation, under an assumption of global Lipschitz constant. To recover the stabilization constant value, some local-in-time convergence analysis has been reported, so that 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, so that the energydissipation property is valid 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, turns out to be 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, so that the stabilization parameter value could be theoretically justified. This justification in turn ensures the energy dissipation at the next time step, so that the mathematical induction could be effectively applied, and the global-in-time energy estimate is accomplished. This technique is expected to be available for many other Runge-Kutta numerical schemes.
报告人简介： Cheng Wang，University of Massachusetts Dartmouth数学系教授。2000年博士毕业于Temple University，导师为Jian-Guo Liu教授。2000-2003年于Indiana University从事博士后研究工作（Zorn postdoc），合作导师为Roger Temam与Shouhong Wang。2003-2008年在University of Tennessee at Knoxvill担任助理教授。2008年进入UMassD任教至今。Cheng Wang教授的研究领域为偏微分方程的稳定高阶算法机器数值分析。已发表70余篇论文，引用达1800余次，入选ESI高被引论文库。担任国际期刊Numerical Mathematics: Theory, Methods and Applications的编委。
报告邀请人：严阅