A spectral overlay method for dissimilar materials

The spectral overlay method is applied to examine the stress distribution along the interface between the two different materials. The essential feature of the spectral overlay method is that the high resolution of localized steep gradients can be achieved by overlaying a spectral interpolant on a standard finite element mesh. In order to evaluate this method and compare it with conventional finite element method, a test problem with high gradients in Poisson equation has been devised. The results show that this method is very powerful in capturing the shape of the gradient field and its peak value. Solutions for two problems with interfaces between dissimilar materials are then given to illustrate the effectiveness of this method.