A CURVILINEAR SPECTRAL OVERLAY METHOD FOR HIGH-GRADIENT PROBLEMS

The spectral overlay method is extended to domains with curvilinear bo undaries. In the spectral overlay method, high resolution of localized steep gradients is achieved by overlaying a spectral interpolant on a standard finite element mesh. A special integration scheme is develop ed which enables the method to satisfy the patch test for a curvilinea r overlay. Results are compared to closed form solutions with high gra dients and the method is shown to be very powerful in capturing the sh ape of the gradient field and its peak value.