Speaker: Dr. Xu Zhang , Purdue University
Dr. Xu Zhang from Purdue University will be on campus on Friday, February 12, 2016. His talk is scheduled for 3:30 PM in DM 193. The title and abstract follow:
Immersed Finite Element Methods for Interface Problems
Abstract: Simulating a multi-scale/multi-physics phenomenon often involves a domain consisting of different materials. This often leads to the so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if the mesh is aligned with interfaces; otherwise the convergence could be impaired. Immersed finite element (IFE) methods, on the other hand, allow the interface to be immersed in elements, so that Cartesian meshes can be used for problems with non-trivial interface geometry. In this talk, we start with a brief introduction about the basic ideas of IFE methods for the second-order elliptic equation. We will present challenges of classical IFE methods, and introduce some recent advances in designing more accurate and robust IFE schemes. Mathematical convergence theories and some numerical experiments will be presented. At last, we will demonstrate how IFE methods can be applied to more complicated interface model problems.