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

Abstract

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 - 1 ln N ) in an associated norm is established, where N is the number of elements. Numerical experiments complement the theoretical results. Moreover, a rate O ( N - 2 ln 2 N ) in a discrete L ∞ norm, and O ( N - 2 ) in L 2 norm, are observed numerically on the Shishkin mesh.