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In this paper, we analyze the supercloseness result of nonsymmetric interiorpenalty Galerkin (NIPG) method on Shishkin mesh for a singularly perturbedconvection diffusion problem. According to the characteristics of the solutionand the scheme, a new analysis is proposed. More specifically, Gau{\ss} Lobattointerpolation and Gau{\ss} Radau interpolation are introduced inside andoutside the layer, respectively. By selecting special penalty parameters atdifferent mesh points, we further establish supercloseness of almost k + 1order under the energy norm. Here k is the order of piecewise polynomials.Then, a simple post processing operator is constructed. In particular, a newanalysis is proposed for the stability analysis of this operator. On the basisof that, we prove that the corresponding post-processing can make the numericalsolution achieve higher accuracy. Finally, superconvergence can be derivedunder the discrete energy norm. These theoretical conclusions can be verifiednumerically.

Supercloseness of the NIPG method for a singularly perturbed convection diffusion problem on Shishkin mesh