  The local discontinuous Galerkin (LDG) method is studied for a third-order
singularly perturbed problem of the convection-diffusion type. Based on a
regularity assumption for the exact solution, we prove almost $O(N^{-(k+1/2)})$
(up to a logarithmic factor) energy-norm convergence uniformly in the
perturbation parameter. Here, $k\geq 0$ is the maximum degree of piecewise
polynomials used in discrete space, and $N$ is the number of mesh elements. The
results are valid for the three types of layer-adapted meshes: Shishkin-type,
Bakhvalov-Shishkin type, and Bakhvalov-type. Numerical experiments are
conducted to test the theoretical results.
