Speaker：Xu Zhang Mississippi State University
Time：20170526 9:45
Place: Room 1208，School of Mathematical Sciences
Detail:
Simulating a multiscale/multiphysics phenomenon often involves a domain consisting of different materials. This often leads to the socalled 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 embedded in elements, so that Cartesian meshes can be used for problems with nontrivial interface geometry.
In this talk, we start with an introduction about the basic ideas of IFE methods for the secondorder elliptic equation. We will present challenges of conventional 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. Finally, we will demonstrate how IFE methods can be applied to more complicated interface model problems.
