A Finite Element Method for Elasticity Interface Problems with Locally Modified Triangulations.

A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh. The local modifications lead to a quasi-uniform body-fitted mesh from the original Cartesian mesh. The standard finite element theory and implementation are applicable. Numerical examples that involve discontinuous material coefficients and non-homogeneous jump in the flux across the interface demonstrate the efficiency of the proposed method.