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

翻译：本文重点分析一类具有指数边界层的二维奇异摄动对流扩散问题的超逼近性质。针对Bakhvalov型网格，采用分片张量积k次多项式的局部间断伽辽金（LDG）方法。通过构造特殊的二维局部高斯-拉杜投影并引入新型插值方法，在Bakhvalov型网格上实现了最优阶k+1的超逼近。关键在于该超逼近结果与奇异摄动参数无关。