  For singularly perturbed convection-diffusion problems, supercloseness
analysis of finite element method is still open on Bakhvalov-type meshes,
especially in the case of 2D. The difficulties arise from the width of the mesh
in the layer adjacent to the transition point, resulting in a suboptimal
estimate for convergence. Existing analysis techniques cannot handle these
difficulties well. To fill this gap, a novel interpolation is designed
delicately for the first time for the smooth part of the solution, bringing
about the optimal supercloseness result of almost order 2 under an energy norm
for finite element method. Our theoretical result is uniformly in the singular
perturbation parameter and is supported by the numerical experiments.
