  This paper presents the first analysis of parameter-uniform convergence for a
hybridizable discontinuous Galerkin (HDG) method applied to a singularly
perturbed convection-diffusion problem in 2D using a Shishkin mesh. The primary
difficulty lies in accurately estimating the convection term in the layer,
where existing methods often fall short. To address this, a novel error control
technique is employed, along with reasonable assumptions regarding the
stabilization function. The results show that, with polynomial degrees not
exceeding $k$, the method achieves supercloseness of almost $k+\frac{1}{2}$
order in an energy norm. Numerical experiments confirm the theoretical accuracy
and efficiency of the proposed method.
