演讲人Speaker：    纪海峰

题目Title: Immersed Finite Element Methods for Interface Problems

时间Date：2026年5月22日    Time：9:30 - 10:30

地点Venue：H502

内容摘要Abstract：

Interface problems arise in a wide range of applications. Conventional finite element methods typically require the mesh to be fitted to the interface, and thus are inconvenient for problems involving moving interfaces or geometrically complex interfaces. Immersed finite element (IFE) methods are designed to solve interface problems on unfitted meshes. In this talk, we present recent advances in the development and analysis of IFE methods for elliptic and Stokes interface problems. We show that nonconforming IFE methods possess a notable property: the associated IFE basis functions are unisolvent on arbitrary triangles and tetrahedra without any angle restrictions. This feature provides a clear advantage over IFE methods that use nodal values as degrees of freedom. We further establish the optimal approximation properties of the IFE spaces, as well as the stability and optimal convergence for the IFE methods with associated constants independent of both the mesh size and the relative position of the interface with respect to the mesh.

个人简介(About the speaker):

纪海峰，南京邮电大学理学院教授，博士生导师。2015年于南京师范大学获得计算数学博士学位。主要研究界面问题的非拟合网格有限元方法及其预处理算法，主持结题国家自然科学基金和江苏省自然科学基金各一项，目前主持国家自然科学基金面上项目一项，大规模复杂系统数值模拟教育部重点实验室重点项目一项，入选南京邮电大学“华礼人才支持计划”拔尖人才培养对象、江苏省“333高层次人才培养工程”培养对象。在 Numer. Math.、SIAM J. Numer. Anal.、Comput. Methods Appl. Mech. Engrg.、J. Sci. Comput.、J. Comput. Phys.等期刊发表论文多篇。