Academy of Mathematics and Systems Science, CAS Colloquia & Seminars
Speaker:
Prof. Xu Zhang, Purdue University
Inviter:
曹礼群
Title:
Recent Advance on Immersed Finite Element Methods for Interface Problems
Time & Venue:
2015.8.19 10:30-11:30am N702
Abstract:
Many simulations in science and engineering involve multiple materials. If partial differential equations are used to model these simulations, it usually leads to the so‐called interface problems. Classic finite elements methods can solve interface problems satisfactorily if meshes are aligned with interfaces; otherwise the convergence cannot be guaranteed. Immersed finite element (IFE) methods, on the other hand, allow interface to be immersed in elements so that their solution mesh is independent of material interface. Classic IFE methods are usually less accurate around the interface than the rest of simulation domain due to the discontinuity of IFE functions across element boundaries. In this talk, we will introduce two approaches to improve the accuracy in the vicinity of interface. The first one is to modify classic linear/bilinear IFE methods by adding some correction terms at interface edges/faces. The second approach is to design new IFE spaces based on nonconforming finite element functions. Our numerical results demonstrate the effectiveness of these new methods. If time permits, we will briefly talk about the application of these IFE methods to more complicated interface models such as elasticity system, and time dependent PDEs with moving interfaces.
