We study the local discontinuous Galerkin (LDG) method for a singularly perturbed reaction-diffusion problem defined on the unit square in \(\mathbb {R}^2\) . Our key goal is to achieve optimal-order convergence in the balanced-norm that rescales the weight of gradient and boundary jump terms of the energy norm to capture boundary layer behavior. While prior work used central or layer-upwind fluxes for optimal-order balanced-norm error estimates, no such results exist for the prevalent alternating fluxes. In this paper, we design special composite projections and leverage their approximation properties to prove optimal-order balanced-norm error estimates for LDG methods with alternating fluxes. Our analysis covers three typical layer-adapted meshes including two Shishkin-type meshes and a Bakhvalov-type mesh. Error bounds are uniform in the perturbation parameter and improve existing convergence rates by half an order (ignoring logarithmic terms). Numerical experiments validate our theoretical results.
