Weighted error estimates of the continuous interior penalty method for singularly perturbed problems

In this paper, we analyse local properties of the continuous interior penalty (CIP) method for a model convection-dominated singularly perturbed convection–diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows thats locally, the CIP method is comparable to the streamline-diffusion or the discontinuous Galerkin methods.