Immersed finite element method for the elasticity equation with a stabilizer

Abstract

Immersed interface finite element developed for the interface problems. The domain of an interface problem consisted of two different materials, which can be divided by an interface. A typical example of such problems is heat conduction in different materials (discontinuous heat conductivity), or fluid interface problems where the surface tension gives a singular force that is supported only on the interface. The complexity of the interfaces makes it more difficult to develop efficient numerical methods. The solutions often discontinuous or even singular. There are two different approachs in finite element methods to solve interface problems. One is a fitted grid approach, which use grids aligned with the interface, usual finite element method can be applicable for interface problems. However, This fitted grid approachs are not efficient. The other approach is the immersed finite element methods, which allow one to use uniform cartesian grid instead of grid allilgned with the interface.