In this paper, we use Fourier analysis to study the superconvergence of thesemi-discrete discontinuous Galerkin method for scalar linear advectionequations in one spatial dimension . The error bounds and asymptotic errors are demonstrated by various numerical experiments . We then extend the analysis to vector conservation laws, solved using theLax-Friedrichs flux . We prove that the superconsvergence holds with the sameorder. We prove it holds in the same order as the error of order$2k+1$ and a transient error of lower order. In the second approach, as byChalmers and Krivodonova, we compute the error directly by decomposition intophysical and nonphysical modes, and obtain

Author(s) : Sirvan Rahmati, Tianshi Lu

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Keywords : error - order - galerkin - linear - scalar -

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