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In this paper, we focus on analyzing the supercloseness property of atwo-dimensional singularly perturbed convection-diffusion problem withexponential boundary layers. The local discontinuous Galerkin (LDG) method withpiecewise tensor-product polynomials of degree k is applied to Bakhvalov-typemesh. By developing special two-dimensional local Gauss-Radau projections andestablishing a novel interpolation, supercloseness of an optimal order k+1 canbe achieved on Bakhvalov-type mesh. It is crucial to highlight that thissupercloseness result is independent of the singular perturbation parameter.

Supercloseness of the LDG method for a two-dimensional singularly perturbed convection-diffusion problem on Bakhvalov-type mesh