Abstract
In this paper, superconvergence properties of the discontinuous Galerkin method for singularly perturbed two-point boundary-value problems of reaction–diffusion and convection–diffusion types are studied. By using piecewise polynomials of degree k on modified Shishkin mesh, superconvergence error bounds of $$(N^{-1}\ln N)^{k+1}$$ in the discrete energy norm are established, where N is the number of elements. Finally, the convergence result is verified numerically.
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