Higher order uniformly convergent NIPG methods for 1-d singularly perturbed problems of convection–diffusion type

In this paper, a higher order NIPG method on a S-type meshes has been developed and analyzed for the singularly perturbed convection–diffusion problems. We prove that the method is uniformly convergent with order k   in εε-weighted DG energy norm, where k   is the degree of piecewise polynomial in finite element space. Numerical experiments support these theoretical results. Moreover, the numerical results show that the NIPG method has a supercloseness property of order k+1k+1 in associated norm if k is odd. But there is no supercloseness property if k is even.