张庆辉 教授:Stable generalized finite element method (SGFEM) for interface problems with a non-smooth interface

讲座时间 Datetime: 
星期三, 2018/05/16 - 15:0017:00
地点 Venue: 
海滨红楼6号楼二楼会议室
报告人 Speaker: 
张庆辉 教授
单位 Affiliation: 
中山大学 数据科学与计算机学院
报告摘要 Abstract: 

We propose a Stable generalized finite element method (SSGFEM) for interface problems, where the interface has a corner. The SSGFEM employs enrichments of two types: the nodes close to the corner are enriched by singular functions characterizing the singularity of the fundamental solution, while the nodes away from the corner and close to the interface are enriched by a distance based function. Both types of enrichments have been modified by a simple local procedure of ``subtracting the interpolant." We prove that the SSGFEM yields the optimal order of convergence. The numerical experiments presented indicates that the conditioning of the SGFEM is not worse than that of the standard finite element method, and the conditioning is robust with respect to the position of the mesh relative to the interface.