  As a popular stabilization technique, the nonsymmetric interior penalty
Galerkin (NIPG) method has significant application value in computational fluid
dynamics. In this paper, we study the NIPG method for a typical two-dimensional
singularly perturbed convection diffusion problem on a Shishkin mesh. According
to the characteristics of the solution, the mesh and numerical scheme, a new
composite interpolation is introduced. In fact, this interpolation is composed
of a vertices-edges-element interpolation within the layer and a local
$L^{2}$-projection outside the layer. On the basis of that, by selecting
penalty parameters on different types of interelement edges, we further obtain
the supercloseness of almost $k+\frac{1}{2}$ order in an energy norm. Here $k$
is the degree of piecewise polynomials. Numerical tests support our theoretical
conclusion.
