Abstract
In this paper, we apply the post-processing technique to the improvement of the superconvergence of the discontinuous Galerkin method for the nonlinear convection-diffusion equations. We firstly analyze the error estimate and convergence accuracy under <i>L</i><sup>2</sup>-norm, and then demonstrate that the α-order difference quotient of DG error is of order <i>k</i>+3/2-<i>α</i>/2 when the upwind fluxes are used. By the duality argument, we construct an appropriate dual equation, and futher obtain superconvergence results of order in the negative-order norm, namely 2<i>k</i>+3/2-<i>α</i>/2 order superconvergence accuracy. Finally, we choose an appropriate kernel function and apply the SIAC filter to the nonlinear convection-diffusion equation to obtain at least 3<i>k</i>/2+1 order superconvergence for post-processed solutions. All theoretical results are proved by numerical experiments.
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