学 术 报 告

报告题目：Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential

报告人：王成 教授（马萨诸塞大学达特茅斯分校）

报告时间：2021年5月24日上午10点–11点

报告地点：数学研究中心多媒体报告厅

数学与统计学院

2021.5.24

报告摘要：The Cahn-Hilliard model with logarithmic potential is considered, in which the key difficulty has always been associated with the singularity of the logarithmic terms. An energy stable finite difference scheme, which implicitly treats the logarithmic terms, is proposed and analyzed in this talk. In particular, how to ensure the positivity of the logarithmic arguments, so that the numerical scheme is well-defined at a point-wise level, has been a long-standing mathematical challenge. It is proved that, given any numerical solution with a fixed bound at the previous time step, there exists a unique numerical solution that satisfies the given bound (-1,1) at a point-wise level. As a result, the numerical scheme is proven to be well-defined, and the unique solvability and energy stability could be established with the help of convexity analysis. In addition, an optimal rate convergence analysis could be appropriately established. Some numerical results are also presented in the talk.

报告人简介：王成，1993年毕业于中国科技大学获数学学士学位，2000年在美国坦普尔大学获得博士学位。2000-2003年在美国印尼安纳大学做博士后，2003-2008年在美国田纳西大学任助理教授，2008-2012年在美国麻省大学达特茅斯分校任助理教授，2012年晋升为副教授。主要研究领域是应用数学，包括数值分析、偏微分方程、流体力学、计算电磁学等。在Journal of Computational Physics，SIAM Journal on Numerical Analysis，IMA Journal of Numerical Analysis等期刊上发表论文100余篇。