Frenet immersed finite element methods for interface problems: Design, analysis and future directions

Speaker: Haroun Meghaichi (OSU)
Dates: 2024/08/29
Location: MW 154
Abstract: In this talk, I will go over a brief survey of unfitted methods for interface problems with an emphasis on the immersed finite element method. Next, I will describe a new approach for designing high-order geometry-conforming IFE spaces based on an “isoparametric” transformation, where the interface is mapped locally to a line segment and the IFE basis functions satisfy the interface conditions exactly. Although the talk will focus mostly on elliptic interface problems, I will provide potential future research directions for parabolic and hyperbolic interface problems to showcase the versatility of the method.