Tuesday, September 15, 2015 at 3:00 PM in SAS 4201
Cory Hauck, Oak Ridge National Lab
Tuesday, October 13, 2015 at 3:00 PM in SAS 4201
Xu Zhang, Purdue
Recent Advance on Immersed Finite Element Methods for Interface Problems
In science and engineering, many simulations 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 linear/bilinear IFE methods are usually less accurate near 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 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. Optimal a priori error estimates are established for both approaches. Our numerical results demonstrate the features of these new methods.
Tuesday, November 17, 2015 at 3:00 PM in SAS 4201
Jingwei Hu, Purdue University
Wednesday, November 18, 2015 at 3:00 PM in SAS 4201
Qi Wang, U of South Carolina
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