Tuesday, Feb 9, 2016 - 3:30pm - Allen 14
Immersed finite element methods for interface problems
Dr. Xu Zhang, Mathematics , Purdue University
Title: 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 so-called interface problems of partial differential equations. Classical finite elements methods can solve interface problems satisfactorily if meshes are aligned with interfaces; otherwise the convergence could be impaired. Immersed finite element (IFE) methods, on the other hand, allow 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.