The local discontinuous Galerkin method on layer-adapted meshes for time-dependent singularly perturbed convection-diffusion problems

In this paper we analyze the error as well for semi-discretization full discretization of a time-dependent convection-diffusion problem. We use in space local discontinuous Galerkin (LDG) method on class layer-adapted meshes including Shishkin-type and Bakhvalov-type implicit θ-scheme time. For piecewise tensor-product polynomials degree k obtain uniform or almost estimates with respect to order k+1/2 some energy norm optimal Our analysis is based careful approximation Ritz projection related stationary problem anisotropic used. discuss also improved one-dimensional case Numerical experiments are given support our theoretical results.