  In this paper, by introducing a reconstruction operator based on the Legendre
moments, we construct a reduced discontinuous Galerkin (RDG) space that could
achieve the same approximation accuracy but using fewer degrees of freedom
(DoFs) than the standard discontinuous Galerkin (DG) space. The design of the
``narrow-stencil-based'' reconstruction operator can preserve the local data
structure property of the high-order DG methods. With the RDG space, we apply
the local discontinuous Galerkin (LDG) method with the implicit-explicit time
marching for the nonlinear unsteady convection-diffusion-reaction equation,
where the reduction of the number of DoFs allows us to achieve higher
efficiency. In terms of theoretical analysis, we give the well-posedness and
approximation properties for the reconstruction operator and the $L^2$ error
estimate for the semi-discrete LDG scheme. Several representative numerical
tests demonstrate the accuracy and the performance of the proposed method in
capturing the layers.
