The immersed finite element method based on a uniform Cartesian mesh has been developed for the linear elasticity equations with discontinuous coefficients 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. The interface is represented by a level set function. Numerical examples are also presented.
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