Abstract
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 L2 norm. In addition, superconvergence of orders k + 2 and k + 1 is obtained for the error and its derivative at generalized Radau points. All the theoretical findings are confirmed by numerical experiments.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11971132, U1637208, 71773024, 51605114 and 11501149) and the National Key Research and Development Program of China (Grant No. 2017YFB1401801).
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Liu, X., Zhang, D., Meng, X. et al. Superconvergence of local discontinuous Galerkin methods with generalized alternating fluxes for 1D linear convection-diffusion equations. Sci. China Math. 64, 1305–1320 (2021). https://doi.org/10.1007/s11425-019-1627-7
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DOI: https://doi.org/10.1007/s11425-019-1627-7