A uniformly convergent continuous–discontinuous Galerkin method for singularly perturbed problems of convection–diffusion type

In this paper, we introduce a coupled approach of local discontinuous Galerkin and standard finite element method for solving singularly perturbed convection–diffusion problems. On Shishkin mesh with linear elements, a rate O(N-1lnN)O(N-1lnN) in an associated norm is established, where N   is the number of elements. Numerical experiments complement the theoretical results. Moreover, a rate O(N-2ln2N)O(N-2ln2N) in a discrete L∞ norm, and O(N-2)O(N-2) in L2 norm, are observed numerically on the Shishkin mesh.