Higher order uniformly convergent continuous/discontinuous Galerkin methods for singularly perturbed problems of convection-diffusion type

In this paper, we propose and analyze a higher order continuous/discontinuous Galerkin methods for solving singularly perturbed convection-diffusion problems. Based on piecewise polynomial approximations of degree k⩾1k⩾1, a uniform convergence rate O(N−klnkN) in associated norm is established on Shishkin mesh, where N is the number of elements. Numerical experiments complement the theoretical results.