学 术 报 告

报告题目：Optimal rate convergence analysis and error estimate of a finite difference scheme for the Ericksen-Leslie  system with the penalty function

报告人：王成 教授  （马萨诸塞大学达特茅斯分校）

报告时间：12月25 日上午10点 – 11点

报告地点： 数学研究中心多媒体报告厅 （线上报告）

数学与统计学院

2020.12.23

报告摘要：A first order accurate in time, finite difference scheme is proposed and analyzed for the Ericksen-Leslie system, which describes motions of nematic liquid crystals. For the penalty function to approximate the phase field constraint, a convex-concave decomposition for the corresponding energy functional is applied. In addition, appropriate semi-implicit treatments are adopted to the convection terms, for both the velocity vector and orientation vector, as well as the the coupled elastic stress terms. In turn, all the semi-implicit terms could be represented as a linear operator of a vector potential, and its combination with the convex splitting discretization for the penalty function leads to a unique solvability analysis for the proposed numerical scheme. Furthermore, a careful estimate reveals an unconditional energy stability of the numerical system, composed of the kinematic energy and internal elastic energies. More importantly, an optimal rate convergence analysis and error estimate for the numerical scheme, which will be the first such result in the area.

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。