报告题目：Quasi-uniform Convergence Analysis of FEMs for the Fourth Order Singularly Perturbed Bi-wave Problem
报告时间：2023年12月7日上午9:30-10:30
报告地点：红瓦楼 826
报告人：石东洋 教授 （烟台大学/郑州大学 ）
报告摘要：In this talk, we will present some new developments on uniform error estimates of the fourth order singularly perturbed Bi-wave problem with conforming and nonconforming elements. Numerical experiments are provided to illustrate the theoretical analysis.
报告人简介：西安交通大学理学博士、东京工业大学博士后。烟台大学黄海学者特聘教授。河南省首批特聘教授（2003年）、郑州大学首批二级教授（2010年）、博士生导师（2000年）、省级重点学科——计算数学学科带头人、学科特聘教授、河南省学术与技术带头人、河南省优秀专家、河南省高层次人才，河南省创新人才培养工程专家、河南省数学首席科普专家、河南省优秀教师、河南省首批优秀研究生指导教师（2022年）。连续主持国家自然科学基金7项（其中，面上6项），省部级项目8项，发表SCI论文200余篇，培养毕业硕士、博士130余人，主编《数值计算方法》，参编国家《数学大辞典》。获“中国百篇最具影响国内学术论文”2次。获省优秀科技成果及论文奖20项（其中一等奖12项）。2021年获河南省自然科学奖二等奖（数学仅此一项）。
报告题目：Structure-preserving discretization for the Poisson—Nernst—Planck equations
报告时间：2023年12月7日上午10:30-11:30
报告地点：红瓦楼 826
报告人：周圣高 副教授 （上海交通大学 ）
报告摘要：The Poisson—Nernst—Planck (PNP) equations have been widely used in the simulations of biomolecular systems. This talk proposes novel second-order discretization in time and finite volume discretization in space for modified PNP equations that incorporate effects arising from ionic steric interactions and dielectric inhomogeneity. A multislope method on unstructured meshes is proposed to reconstruct positive, accurate approximations of mobilities on faces of control volumes. Numerical analysis proves that the proposed numerical schemes are able to unconditionally ensure the existence of positive numerical solutions, original energy dissipation, mass conservation, and preservation of steady states at discrete level. Extensive numerical simulations are conducted to demonstrate numerical accuracy and performance in preserving properties of physical significance. Applications in ion permeation through a 3D nanopore show that the modified PNP model, equipped with the proposed schemes, has promising applications in the investigation of ion selectivity and rectification. The proposed second-order discretization can be extended to design temporal second-order schemes with original energy dissipation for a type of gradient flow problems with entropy.
报告人简介：周圣高，上海交通大学长聘副教授。2012年博士毕业于浙江大学，主要从事分子体系的可计算建模、分析与计算。相关研究成果发表于PNAS，ACS Energy Lett., Math. Comput., SIAM系列等。
报告邀请人：黄学海 教授