Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations
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This paper investigates superconvergence properties of the local discontinuous Galerkin methods with generalized alternating fluxes for one-dimensional linear convection-diffusion equations. By the technique of constructing some special correction functions, we prove the (2k+1)th order superconvergence for the cell averages, and the numerical traces in the discrete L^2 norm. In addition, superconvergence of order k+2 and k+1 are obtained for the error and its derivative at generalized Radau points. All theoretical findings are confirmed by numerical experiments.
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