Abstract
In this study, the focus is on exploring the supercloseness property of the local discontinuous Galerkin (LDG) method in the context of a singularly perturbed convection–diffusion problem on Bakhvalov-type mesh. By developing specialized local Gauss–Radau projections in the two-dimensional case, and establishing a novel interpolation premised on the special projections, supercloseness of an optimal order k+1 can be achieved on Bakhvalov-type mesh. Notably, the obtained result remains unaffected by the singular perturbation parameter ɛ, indicating that the limitations encountered in previous studies, where the supercloseness results on Bakhvalov-type mesh were always impacted by the logarithmic factor ln1ɛ are overcome.
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