An Immersed FEM for Elasticity Equations with Interfaces

The immersed finite element method based on a uniform Cartesian mesh has been developed for elasticity equations with discontinuous physical parameters across an interface in this paper. The interface does not have to be aligned with the mesh. The main idea is to modify the basis function over those triangles in which the interface cuts through so that the natural interface conditions are satisfied. The standard linear basis functions are used for other triangles. A level set function whose zero level set represent the interface is used. Numerical examples are also presented. 2000 AMS Mathematics Subject Classification: 65N06, 74B10, 74S30.