  In this paper, we analyze the supercloseness result of nonsymmetric interior
penalty Galerkin (NIPG) method on Shishkin mesh for a singularly perturbed
convection diffusion problem. According to the characteristics of the solution
and the scheme, a new analysis is proposed. More specifically, Gau{\ss} Lobatto
interpolation and Gau{\ss} Radau interpolation are introduced inside and
outside the layer, respectively. By selecting special penalty parameters at
different mesh points, we further establish supercloseness of almost k + 1
order under the energy norm. Here k is the order of piecewise polynomials.
Then, a simple post processing operator is constructed. In particular, a new
analysis is proposed for the stability analysis of this operator. On the basis
of that, we prove that the corresponding post-processing can make the numerical
solution achieve higher accuracy. Finally, superconvergence can be derived
under the discrete energy norm. These theoretical conclusions can be verified
numerically.
