Optimal Balanced-Norm Error Estimate of the LDG Method for Singularly Perturbed Reaction-Diffusion Problems in Two Dimensions with Layer-Upwind Flux

The paper presents an optimal-order balanced-norm error analysis of the local discontinuous Galerkin (LDG) method for solving singularly perturbed reaction-diffusion problems in two dimensions. The key innovation is the introduction of a new "layer-upwind flux" in the LDG discretization, which leads to an optimal-order error bound in a balanced norm without the need for penalty terms.