IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Recent advance of immersed finite element methods for interface problems

  • April 16, 2018
  • 2:15 p.m.
  • LeConte 312

Abstract

Simulating a 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 provided that the mesh is aligned with interfaces. Immersed finite element methods (IFEM), on the other hand, allow the interface to be immersed in elements, so that unfitted meshes such as Cartesian meshes can be used for problems with non-trivial interface geometry.

In this talk, we start with an introduction about the basic ideas of IFEM for the second-order elliptic equation. We will present challenges of conventional IFEM, and introduce some recent advances in designing more accurate and robust IFE schemes. A posteriori error estimation for IFEM and its adaptive mesh refinement will also be presented. Finally, we will demonstrate how these IFEM can be applied to other interface model problems.

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